I have a web app that uses a connection string and SSI to connect to a database.

Example:
<%
Option Explicit
Dim strConnect
%>

<!-- METADATA TYPE="typelib"
             FILE="c:\program files\common files\system\ado\msado15.dll" -->

In turn, the include file specifies a DSN connection like so:
<%
strConnect = "DSN=DSN1;User Id=username;Password=password;"
%>

Is it possible to connect to more than one datasource at the same time using the SSI, or can I specify another SSI include on the same page as the top include?

Yep. I use a single SSI for all of my connection strings so I can connect to multiple databases within my app.