You'll probably want to separate them, especially if their functionality in the pre/post executes differs. Try to organize your code into logical blocks. For example, if you have an Async Task to Login, and an Async task to, for example, download lots of document data via JSON, they will want separate Async tasks.
However, lets say you have two separate API calls that return similar or partially the same data - if one returned the details of a file (name, size) and the other returned the same data but was a revision of a file - you could switch these in the same ASYNC because the post execute is going to perform the same (or partially the same) code to extract data from the JSON.