As a 3P, you can upgrade domestic flights using e500 upgrades. You earn four e500s for every 10K BIS miles you fly on UA or UX metal - each is good for 500 miles. For example, you'd need 4 e500s to upgrade a flight between 1550-2050 miles (UA gives a 50 mile cushion). You should be able to request upgrades on-line - sometimes they clear, sometimes they don't.

If you're flying on Y or B fares domestically, as an elite member you can be put on the complimentary upgrade list - these upgrades clear in a process similar to the e500s.