Is it possible for a technician to submit a request using a template assigned to another support group?

For example, if a technician from the software development team needs to submit a request to the software team.

Currently, I'm not seeing any templates except the ones specifically for the technician's support group(s).  I wouldn't expect that technician to be able to work on a request not in their group but they should be able to submit requests for other groups as if they were a requester.

Thank you.