I'm not sure what your reasoning is here. Why would you want to juggle all that? Your DBConnect will need, for each target database, proper connection strings as well as proper SQL queries to retrieve data. Each database will have distinct data and distinct queries.
Even if you are, for example, querying production and UAT version s of the same database, you are much better off procedurally setting those up as separate connections, so that you can make sure they each get ingested into the appropriate indexes.
imho you have to create a connection for each database.
how can you connect to multiple servers (with multiple unique databases in them) with a single connection?
would love to learn i am mistaking here, but to your first question, the answer in my opinion is: "no".
as for the second question regarding limitations of db server connections, do you mean from the splunk DB Connect app side?? or from the db server side?
as for your suggestion request, like mentioned above, would love to learn i am wrong here, but i dont think there is a way.
hope it helps