There are a variety of ways you might model this, and different ways that your existing system can be translated into Sample Manager.

I do want to address here that it's not true that Sources can only have 1-1 relationships with Sample Types. You can't have two File Import Column Names that are the same as each other in one Sample Type definition, but you can certainly have sources of as many types as you like and use their different names.
For example, if your "TEST##" Sources all themselves have parents of type "Patient" and "Visit", you could use ancestor naming patterns to incorporate those values, OR if the sample data now has associated Patient and Visit detail, that can be used both to generate the sample names and create the lineage you want in your sample sources.

Rather than go through various options here, I think the best next step here is to connect you directly with our Sample Manager trial support process. I'll reach out via email to make that connection.

--Molly