It is perfectly fine to have a user in more than one group, and even to have them be on call for more than one group at a time. Try creating the oncall schedule for each group so that all of your groups have the coverage they need (i.e the right person is scheduled to handle the issue at the right time for that group).
Note also, that if no-one is on call for the schedule, the group escalation policy can be configured to notify everyone, or individuals as well, outside of the schedule, and there is always an ending step which will auto-assign/acknowledge or close the alert if no-one was notified and/or has acknowledged the alert.