Can we use "other" with a plural noun even if it is preceded by an indefinite pronoun like any, some, each?
It doesn't sound natural. I'd say, "All other routes to Boston take longer; Any other route to Boston takes longer."
But yes you can certainly use 'other' with a plural, eg. "Other people might not agree."
You can use "Some other + plural". "Spot is black and white. Some other dogs are single-coloured."
You can use "Any other + plural". (At least in AusE; this might vary.)
You can't use "Each other + plural."