In my opinion, You can have as many asynctask as you want, its becous of one fact:
AsyncTask allows you to perform asynchronous work on your user interface. It performs the blocking operations in a worker thread and then publishes the results on the UI thread, without requiring you to handle threads and/or handlers yourself.
The second fact is :
When first introduced, AsyncTasks were executed serially on a single background thread. Starting with DONUT, this was changed to a pool of threads allowing multiple tasks to operate in parallel. Starting with HONEYCOMB, tasks are executed on a single thread to avoid common application errors caused by parallel execution. ;)
I have a little experience with AsyncTask, so my answer for your question can be wrong.