Is there a way to put multiple groups into another group?
No, but you can put them into a Matrix.
It’s been a feature request in the past unless I’m mistaken. What Scott said, but also you can burn an input channel, set the input of that channel to be the output of the desired inception group, then send that input channel to a group. …effectively giving you a group within a group.
You can put groups into an Aux or Matrix
In the past, with analogue consoles, you could always do anything you wanted. But even with them there was no solution to route a subgroup directly into another subgroup. And it was precisely for such applications that the matrix was invented.
The nice thing about a matrix is that you can use it as a collecting basin for all kinds of signals. No matter if they are subgroups, or aux paths, or since some time also single inputs.
The simple solution to your problem could be to use a matrix instead of a “master subgroup”.