One reason I usually end up taking polymath is that there are all sorts of little tasks that make me wish I had just one more skill. I come across bodies in dungeons and Main Story maps, I come across potentially valuable rocks, I want to build a robot, whatever. If I get lucky, I'll find a lancemate that has such a skill. If I'm determined I could go around hiring and then dismissing all the available mercenaries looking for one with the skill. But wouldn't it be a neat addition if you could just go out and hire someone with Medicine?
I'm proposing something along these lines: each city has some random NPC "specialists for hire". They'd have high levels in one particular skill - Medicine, say - and be expensive in proportion to the level ($100*XP to get that level maybe?). They'd have minimal other skills, in particular no particular combat skills, and they would come with no mech or armor but some skill-related equipment. You'd hire them and they'd become a normal lancemate (and require a lancemate slot) so that you'd then have access to whatever skill they had. There would be rumours in the mix ("I hear doctor so-and-so makes house calls" or "I hear professor such-and-such will do field work") letting you know about the existence of such people in each location.
This would let people who need Science just to figure out that one plot point they're curious about (what's really going on in that Venusian ship?) hire a scientist, who they'd then have to carefully protect, for the duration of one mission. You could theme the cities a little by making the best scientists available for hire at Galconde, while at Cayley there might be only level-1 scientists, and none at Tohru (say). For skills that you want around in your party, say Medicine, you could hire someone and then carefully accumulate them enough XP to raise their combat levels to something that will keep them alive.
You can sort of do this with mercenaries now, but you're buying a pig in a poke - as far as I can tell there's no way to tell what if any useful skills they'll have. It's also sort of present in the "forensic investigator for hire" option for people who don't have Insight, but that only works for skills where you can bring the object of interest in for investigation. In any case I don't think this idea would require much in the way of new game mechanics, and it would (it seems to me) alleviate the feeling of needing every skill "just in case" as well as adding flavour to the game and new tactics to the combat ("how do I keep this very fragile doctor out of combat but close enough to cure my poison?").
