Is it possible to allow write access to multiple users on QuickBlox framework?
Yes, it is possible to allow write access to multiple users.
QuickBlox released iOS SDK 1.7 with Permissions API, please check more details here http://quickblox.com/developers/SimpleSample-customObjects-ios#Permissions
The same you can find for Android http://quickblox.com/developers/SimpleSample-customObjects-android#Permissions
REST API documentation can be found here http://quickblox.com/developers/Custom_Objects#Permissions
With this you can easily grant access to records to your users, as well as specify what operations are allowed (READ, CREATE, UPDATE, DELETE).