I can say from experience that for a revenue (non-award) ticket, it's possible to put the UA segments on hold and then call to add another carrier's segment to the itinerary. The agent may put you on hold for a while so that the rate desk can help them price it, but it might be straightforward enough for them to give you an immediate answer. This all depends on the UA fare being combinable with the other carrier's fare (so it's subject to UA's and AS' fare rules, I believe). Another option, if you can't get the hold option to work for you, is to buy the ticket through United.com with only the UA segments and call within 24 hours of booking (but after ticketing) to have the second carrier's segments added. They will reprice the itinerary and reissue your ticket without a change fee (again, within 24 hours). If this doesn't work, you can always cancel for a full refund and book some other way.

If you have anything close to a tight connection, it would be beneficial for you to have everything on one itinerary so that if the inbound international flight is delayed and immigration takes too long, the carrier will be obligated to put you on another flight to your destination. One separate tickets, you will probably need to buy a new ticket at a walk-up price.