Is it possible to integrate additional company codes into Finmatics after system setup?

Yes, the integration of new company codes is easily possible with a few clicks.

You are a user of the administrator or accountant type. Click on Client,
and select the client for which you want to create a company code. Then click on Processes.
Click ADD to add a new company code and provide name, company code type and verbose name.

It is also possible to create new company codes using the REST API (put requests).