From what I can tell/the last production I saw:
Grumio-EIE (maybe ILE)
Kate-SLE? LSI? Leaning LSI. I suppose ESI is also a possibility.
Baptista-not really enough info to type him, but I'd suppose ESE? I dunno.
Meh. The characters in this one aren't terribly vivid; they're more stock types. Gremio is more "horny old guy" than any particular type; Hortensio is more "socially awkward suitor" than any particular type (although it's easy to associate with some sort of IT type, a precursor to Malvolio in some ways); Lucentio and Bianca are more "standard pair of lovers" than any particular type. Bianca seems like an NF though, leaning EIE over IEI, but IEI's a possibility too. Or maybe delta NF? I dunno.
Not a rule, just a trend.
IEI. Probably Fe subtype. Pretty sure I'm E4, sexual instinctual type, fairly confident that I'm a 3 wing now, so: IEI-Fe E4w3 sx/so. Considering 3w4 now, but pretty sure that 4 fits the best.
Yes 'a ma'am that's pretty music...
I am grateful for the mystery of the soul, because without it, there could be no contemplation, except of the mysteries of divinity, which are far more dangerous to get wrong.