diff --git a/scripts/langindex.json b/scripts/langindex.json
index e8a39aa49..153d195fc 100644
--- a/scripts/langindex.json
+++ b/scripts/langindex.json
@@ -131,6 +131,10 @@
   "addon.messages.blockcontact": "message",
   "addon.messages.blockcontactconfirm": "local_moodlemobileapp",
   "addon.messages.blocknoncontacts": "message",
+  "addon.messages.contactableprivacy": "message",
+  "addon.messages.contactableprivacy_coursemember": "message",
+  "addon.messages.contactableprivacy_onlycontacts": "message",
+  "addon.messages.contactableprivacy_site": "message",
   "addon.messages.contactlistempty": "local_moodlemobileapp",
   "addon.messages.contactname": "local_moodlemobileapp",
   "addon.messages.contacts": "message",
@@ -1269,7 +1273,6 @@
   "core.fileuploader.uploading": "local_moodlemobileapp",
   "core.fileuploader.uploadingperc": "local_moodlemobileapp",
   "core.fileuploader.video": "local_moodlemobileapp",
-  "core.login.findyoursite": "local_moodlemobileapp",
   "core.folder": "moodle",
   "core.forcepasswordchangenotice": "moodle",
   "core.fulllistofcourses": "moodle",
@@ -1329,6 +1332,7 @@
   "core.login.erroraccesscontrolalloworigin": "local_moodlemobileapp",
   "core.login.errordeletesite": "local_moodlemobileapp",
   "core.login.errorupdatesite": "local_moodlemobileapp",
+  "core.login.findyoursite": "local_moodlemobileapp",
   "core.login.firsttime": "moodle",
   "core.login.forgotten": "moodle",
   "core.login.getanothercaptcha": "auth",
diff --git a/src/addon/messages/lang/en.json b/src/addon/messages/lang/en.json
index a75924db0..c89f8ccf8 100644
--- a/src/addon/messages/lang/en.json
+++ b/src/addon/messages/lang/en.json
@@ -3,6 +3,10 @@
     "blockcontact": "Block contact",
     "blockcontactconfirm": "You will no longer receive messages from this contact.",
     "blocknoncontacts": "Prevent non-contacts from messaging me",
+    "contactableprivacy": "Accept messages from:",
+    "contactableprivacy_coursemember": "My contacts and anyone in my courses",
+    "contactableprivacy_onlycontacts": "My contacts only",
+    "contactableprivacy_site": "Anyone on the site",
     "contactlistempty": "The contact list is empty",
     "contactname": "Contact name",
     "contacts": "Contacts",
diff --git a/src/addon/messages/pages/settings/settings.html b/src/addon/messages/pages/settings/settings.html
index 8c0f58441..fbdbabf1d 100644
--- a/src/addon/messages/pages/settings/settings.html
+++ b/src/addon/messages/pages/settings/settings.html
@@ -8,12 +8,28 @@
         <ion-refresher-content pullingText="{{ 'core.pulltorefresh' | translate }}"></ion-refresher-content>
     </ion-refresher>
     <core-loading [hideUntil]="preferencesLoaded">
-        <!-- Block non contacts. -->
+        <!-- Contactable privacy. -->
         <ion-card>
-            <ion-item>
+            <ion-item *ngIf="!advancedContactable">
               <ion-label>{{ 'addon.messages.blocknoncontacts' | translate }}</ion-label>
-              <ion-toggle [(ngModel)]="blockNonContactsState" (ionChange)="blockNonContacts(blockNonContactsState)"></ion-toggle>
+              <ion-toggle [(ngModel)]="contactablePrivacy" (ionChange)="saveContactablePrivacy(contactablePrivacy)"></ion-toggle>
             </ion-item>
+
+            <ion-list *ngIf="advancedContactable" text-wrap radio-group [(ngModel)]="contactablePrivacy" (ionChange)="saveContactablePrivacy(contactablePrivacy)">
+                <ion-item-divider color="light">{{ 'addon.messages.contactableprivacy' | translate }}</ion-item-divider>
+                <ion-item>
+                    <ion-label>{{ 'addon.messages.contactableprivacy_onlycontacts' | translate }}</ion-label>
+                    <ion-radio [value]="onlyContactsValue"></ion-radio>
+                </ion-item>
+                <ion-item>
+                    <ion-label>{{ 'addon.messages.contactableprivacy_coursemember' | translate }}</ion-label>
+                    <ion-radio [value]="courseMemberValue"></ion-radio>
+                </ion-item>
+                <ion-item *ngIf="allowSiteMessaging">
+                    <ion-label>{{ 'addon.messages.contactableprivacy_site' | translate }}</ion-label>
+                    <ion-radio [value]="siteValue"></ion-radio>
+                </ion-item>
+            </ion-list>
         </ion-card>
 
         <ng-container *ngIf="preferences">
diff --git a/src/addon/messages/pages/settings/settings.ts b/src/addon/messages/pages/settings/settings.ts
index 72a4e0b26..05e87edb6 100644
--- a/src/addon/messages/pages/settings/settings.ts
+++ b/src/addon/messages/pages/settings/settings.ts
@@ -17,6 +17,7 @@ import { IonicPage } from 'ionic-angular';
 import { AddonMessagesProvider } from '../../providers/messages';
 import { CoreUserProvider } from '@core/user/providers/user';
 import { CoreDomUtilsProvider } from '@providers/utils/dom';
+import { CoreSitesProvider } from '@providers/sites';
 
 /**
  * Page that displays the messages settings page.
@@ -31,10 +32,21 @@ export class AddonMessagesSettingsPage implements OnDestroy {
 
     preferences: any;
     preferencesLoaded: boolean;
-    blockNonContactsState = false;
+    contactablePrivacy: number | boolean;
+    advancedContactable = false; // Whether the site supports "advanced" contactable privacy.
+    allowSiteMessaging = false;
+    onlyContactsValue = AddonMessagesProvider.MESSAGE_PRIVACY_ONLYCONTACTS;
+    courseMemberValue = AddonMessagesProvider.MESSAGE_PRIVACY_COURSEMEMBER;
+    siteValue = AddonMessagesProvider.MESSAGE_PRIVACY_SITE;
+
+    protected previousContactableValue: number | boolean;
 
     constructor(private messagesProvider: AddonMessagesProvider, private domUtils: CoreDomUtilsProvider,
-            private userProvider: CoreUserProvider) {
+            private userProvider: CoreUserProvider, sitesProvider: CoreSitesProvider) {
+
+        const currentSite = sitesProvider.getCurrentSite();
+        this.advancedContactable = currentSite && currentSite.isVersionGreaterEqualThan('3.6');
+        this.allowSiteMessaging = currentSite && currentSite.canUseAdvancedFeature('messagingallusers');
     }
 
     /**
@@ -54,7 +66,8 @@ export class AddonMessagesSettingsPage implements OnDestroy {
     protected fetchPreferences(): Promise<any> {
         return this.messagesProvider.getMessagePreferences().then((preferences) => {
             this.preferences = preferences;
-            this.blockNonContactsState = preferences.blocknoncontacts;
+            this.contactablePrivacy = preferences.blocknoncontacts;
+            this.previousContactableValue = this.contactablePrivacy;
         }).catch((message) => {
             this.domUtils.showErrorModal(message);
         }).finally(() => {
@@ -85,19 +98,31 @@ export class AddonMessagesSettingsPage implements OnDestroy {
     }
 
     /**
-     * Block non contacts.
+     * Save the contactable privacy setting..
      *
-     * @param {boolean} block If it should be blocked or not.
+     * @param {number|boolean} value The value to set.
      */
-    blockNonContacts(block: boolean): void {
+    saveContactablePrivacy(value: number | boolean): void {
+        if (this.contactablePrivacy == this.previousContactableValue) {
+            // Value hasn't changed from previous, it probably means that we just fetched the value from the server.
+            return;
+        }
+
         const modal = this.domUtils.showModalLoading('core.sending', true);
-        this.userProvider.updateUserPreference('message_blocknoncontacts', block ? 1 : 0).then(() => {
+
+        if (!this.advancedContactable) {
+            // Convert from boolean to number.
+            value = value ? 1 : 0;
+        }
+
+        this.userProvider.updateUserPreference('message_blocknoncontacts', value).then(() => {
             // Update the preferences since they were modified.
             this.updatePreferencesAfterDelay();
+            this.previousContactableValue = this.contactablePrivacy;
         }).catch((message) => {
             // Show error and revert change.
             this.domUtils.showErrorModal(message);
-            this.blockNonContactsState = !this.blockNonContactsState;
+            this.contactablePrivacy = this.previousContactableValue;
         }).finally(() => {
             modal.dismiss();
         });
@@ -148,7 +173,7 @@ export class AddonMessagesSettingsPage implements OnDestroy {
      *
      * @param {any} refresher Refresher.
      */
-    refreshEvent(refresher: any): void {
+    refreshPreferences(refresher: any): void {
         this.messagesProvider.invalidateMessagePreferences().finally(() => {
             this.fetchPreferences().finally(() => {
                 refresher.complete();
diff --git a/src/addon/messages/providers/messages.ts b/src/addon/messages/providers/messages.ts
index 4957047d4..17b907a11 100644
--- a/src/addon/messages/providers/messages.ts
+++ b/src/addon/messages/providers/messages.ts
@@ -37,6 +37,10 @@ export class AddonMessagesProvider {
     static POLL_INTERVAL = 10000;
     static PUSH_SIMULATION_COMPONENT = 'AddonMessagesPushSimulation';
 
+    static MESSAGE_PRIVACY_COURSEMEMBER = 0; // Privacy setting for being messaged by anyone within courses user is member of.
+    static MESSAGE_PRIVACY_ONLYCONTACTS = 1; // Privacy setting for being messaged only by contacts.
+    static MESSAGE_PRIVACY_SITE = 2; // Privacy setting for being messaged by anyone on the site.
+
     protected logger;
 
     constructor(logger: CoreLoggerProvider, private sitesProvider: CoreSitesProvider, private appProvider: CoreAppProvider,
@@ -469,7 +473,7 @@ export class AddonMessagesProvider {
 
             return site.read('core_message_get_user_message_preferences', {}, preSets).then((data) => {
                 if (data.preferences) {
-                    data.preferences.blocknoncontacts = !!data.blocknoncontacts;
+                    data.preferences.blocknoncontacts = data.blocknoncontacts;
 
                     return data.preferences;
                 }
diff --git a/src/assets/lang/en.json b/src/assets/lang/en.json
index ba1ffd309..40750d05f 100644
--- a/src/assets/lang/en.json
+++ b/src/assets/lang/en.json
@@ -131,6 +131,10 @@
     "addon.messages.blockcontact": "Block contact",
     "addon.messages.blockcontactconfirm": "You will no longer receive messages from this contact.",
     "addon.messages.blocknoncontacts": "Prevent non-contacts from messaging me",
+    "addon.messages.contactableprivacy": "Accept messages from:",
+    "addon.messages.contactableprivacy_coursemember": "My contacts and anyone in my courses",
+    "addon.messages.contactableprivacy_onlycontacts": "My contacts only",
+    "addon.messages.contactableprivacy_site": "Anyone on the site",
     "addon.messages.contactlistempty": "The contact list is empty",
     "addon.messages.contactname": "Contact name",
     "addon.messages.contacts": "Contacts",
diff --git a/src/classes/site.ts b/src/classes/site.ts
index c545341a2..4b830350a 100644
--- a/src/classes/site.ts
+++ b/src/classes/site.ts
@@ -214,7 +214,8 @@ export class CoreSite {
         3.2: 2016120500,
         3.3: 2017051503,
         3.4: 2017111300,
-        3.5: 2018051700
+        3.5: 2018051700,
+        3.6: 2018111000 // @todo: Replace it with the right 3.6 date when released.
     };
 
     // Rest of variables.