One CRM per customer, or?

Hi, I have a question. We run a call center within our company through which we call clients of various companies. However, these companies want us to keep their data separate. So we run multiple instances of CRM and in the long run this does not seem sustainable. For example, we now have 6 companies, so we have 6 CRM instances. Is there any CRM on the market that allows you to work with separate databases but at the same time runs as one installation? Or is this a common practice?

Currently, we solve it so that when a lead comes in, we identify within the logic of the collection application which customer it is and then we save this lead into the appropriate CRM so that our operators can handle it.

The ideal situation would be if we have one CRM instance connected to multiple databases. So we would still identify who the lead came from, we would write it to the appropriate database, but the operator would actually be working on one CRM and maybe switching between contexts somewhere in the menu.