Searching Fare Class for One Segment of Multi-Segment Itinerary

Hey all,

I'm looking to use a system-wide upgrade for 2 segments of a 5 segment international itinerary. I believe only the segments which will be upgraded need to be in the mid-high fare classes (W and above) - please correct me if that assumption is wrong because the rest of this will be irrelevant.

Is there a way to search for my itinerary on United.com or elsewhere designating only those particular segments as W class and above (I have the full list of eligible fare classes, no need to give me that) while leaving the remaining segments as "lowest cost." Right now I booked W all the way through, but it occurred to me that I might be able to secure an overall cheaper itinerary while maintaining my ability to use system-wide upgrades on the long segments.

Thanks