I think the engine could support it. My MOBILE computer in my tow truck (Shuttle PC) SIMULTANEOUSLY runs S&T, DeLorme, an AT&T broadband USB connection, a webcam and a PalTalk chat room as well as keeping a browser open for quick "4-1-1" address lookups etc, and it also has MS EXCEL running so I can modify the current job invoice, and the printer is hooked up as well. All at the same time, no problems.
I think S&T could easily keep track of three routes and update them as you drive, and switch the NAV mode to whichever route you are following at the moment.
Example: Last night, I was heading home from a tow. I pulled off of the I-15 freeway northbound to stop at a Carl's Jr. The north and southbound on ramps there were closed for construction and the freeway north of that point was narrowed to one lane with cones. I would have loved to look at the screen and see the other two suggested alternatives without having to clear the route and set the next 3 northbound on ramps to "avoid" before successfully routing a way back onto the freeway.
If the "preferred roads" option was set to avoid freeways, and that route was displayed alongside the other two, I could have easily picked it as my alternate route.