I was looking for a way to handle this some time ago, and found that the good people at NIST had already thought about it a lot more.

They made a tool called ACTS which allows you to specify some variables which affect your testing, then generate a bunch of tests with combinations of just n variables at a time where typically n is 2 or 3 but can be higher, perhaps if you're automating the tests or have exceptional patience.

They have some empirical data on how the chance of finding additional bugs decreases as you increase n.

More info here or by searching for NIST ACTS:

https://csrc.nist.rip/groups/SNS/acts/documents/comparison-r...