As all connections are created at the server side, the number of simultenous connections at any given time to a database could be well controled. In this case, you probably want a connection pool for each database on the server side.

The connections can be kept open all the time (for example created at server start up time) for your first version. In later versions you can try to have better control over size of connections base on demand (even in this case, connections are not created per request, but rather base on the load of the application.)