SQLite Forum

Here is a suggestion:  

Set a counter to 0.  Keep on attaching databases to a connection until you get an error, incrementing the counter by 1 each time you do **not** get an error.  Stop when you get an error that you cannot attach more databases to the connection.  The number in the counter is the number of databases, aside from the main database (#0) that can be attached to a connection.

If you have no automated way of doing this you can do it manually by stokes on a piece of scrap paper, or using fingers (and maybe toes as well).

The number you obtain will not "magically change" by itself without outside influence.