Here few possibilities for TE base spacetug.
LEO to Gateway 45mt tanker launched on NG. This should be lower cost vehicle compared to HLS TE as its only needs to last 3-4day trip to gateway after which its expendable. Rough guess it could deliver 15mt of LH and LOX to gateway.
Earth departure stage for deep space missions. With option of additional topup from tanker at HEO or EML1.
Transport crew between LEO-Gateway-LEO, would need 2xBE7 for redundancy. Crew habitat can be based on LM AE which uses lot of Orion systems. Refuel at Gateway for return trip.