Okay, basically all of my miles (aside from 100,000 AMEX points) are on United Mileage Plus.

I am about to embark on an RTW trip for business (sadly, really only two main stops).

I fly from LAX-NCE (via FRA) on LH in PAID C and know I can try to upgrade with a UA SWU (but only at the gate, subject to availability).

Is there any way for me to upgrade MUC-BKK (from PAID C to F) using my MP miles?

(My final major leg is BKK-LAX, but it is a two class plane, so no need to upgrade)...