AS can and will ticket flights on airlines it has a ticketing agreement with, such as AA, DL, UA, and US, provided:
1. There is an AS fare on the ticket
2. Travel is within the AS's service area (50 US States/Canada/Mexico)
2. The other airline's fare can be combined with the AS fare
3. The agent can find the flights in their reservations system. YMMV on AS being able to ticket AA/DL-marketed, AS-operated codeshares.
If the other airline is an AS partner and AS doesn't typically serve the city pair where one wishes to fly the other airline, it may be possible to book the itinerary on alaskaair.com.
I've booked and flown a few such itineraries, including one with fares from 3 different airlines (DL, AA, and AS) and one with 5 different operating carriers in one direction.