I think we cannot assign multiple request groups to a responsibility.
If you want to access the standard programs/requests from Request_group2, may be you can assign them there are well. or create a new responsibility for both standard and custom programs.
Could not think of any other option.
Thanks for response but we don't want to create a new responsibility.
and want to use both the Request Groups using same responsibility.
I think as PK has already pointed out, you might need to add the custom Concurent Programs to the Request_group1, if you don't want to create a new Request Group of Responsibility