I played around with this tonight on GitLab.com and I think your use case is possible.
You can achieve this with the Merge Request Approvals feature: https://docs.gitlab.com/ee/user/project/merge_requests/merge_request_approvals.html#merge-request-approvals
I tested it out by creating two groups on GitLab.com and creating a project in one of the groups.
Then I went to the Merge Request Approvals in “Settings” and added both groups as approvers and required 2 approvals.
What’s interesting is that initially since I am the only member of both groups and I submitted the MR, no other approvals were required. Since I am a member of both groups that’s technically approval from both groups.
So to test the use case further I added a dummy user and that led to me getting this prompt at the MR page (no change in setting required, just had to add the user)
I’m glad you asked this question, it’s a cool feature I got to learn about!
More reading (and interesting discussion in the comments, including the CEO): https://about.gitlab.com/2015/07/29/feature-highlight-merge-request-approvals/