Can a user group have multiple parent groups?

What is your use case?

In short: a group may be added as a member of multiple other groups, but this is separate from the defined "parent" group within a group's configuration, which is limited to one group.

I am creating different (a) groups based on their roles. And then I want to create different (b) groups based on the Actions.

So my question is if I can add (a) group into multiple (b) groups

Keep in mind you can assign "initiator" rights to multiple in a process model, etc, so you don't need to "roll up" the groups into a parent group for the sake of allowing people to access Actions.

I believe your plan should work -- group-in-group membership works well in Appian and can handle security at a meta level fairly easily. One group can be a member of multiple other groups easily, and one group can have multiple other groups AS members easily also.

I suggest you forget the word "parent" since that's something specific within the group configuration -- instead use "member" and "member of". 

I also suggest you make a whiteboard diagram in advance of the group permission structure you have in mind, just to make sure everything is internally consistent before spending the time to set permissions on process models, etc.  This will largely help prevent the confusion it can create when dealing with multiple group membership nesting.