Does Massachusetts offer any time of additional pet insurance coverage for veterinarian appointments/vaccinations/spaying/etc.

You should be able to get some information on that at your veterinarian :)

Pet insurance just like "people" insurance is sold though private companies. But just like with people insurance you need to be sure your VET accepts the plans offered.

Veterinary Pet Insurance (VPI) - Dog Insurance, Cat Insurance, Pet Health Insurance

ShelterCare Pet Insurance Programs

Pet Insurance Alternative