No way would I design a pier and beam foundation for a cold climate. You’ll have to dig down far enough below the frost that you might as well add that additional basement space to the original basement.

You might want to consider a frost protected shallow foundation. Instead of digging below the frostline, you provide horizontal insulation.

This is the wrong place to be stingy in New England. A crawlspace is a bad idea unless its designed like a half height basement which doesn't save much.

An addition on piers might be a small savings but would be a big loss in control of the space below the floor and resale (such a design is unheard of in New England).. Frost protected footings and a slab would hurt the resale value far more than you could save,

Postpone the addition until you can afford a basement foundation.

And check the credentials of your architect.

A kitchen needs electrical lines, water piping and sewer piping, all which need to be connected to your existing utilities, which are likely in your basement. No better place to put them but a crawl space. A full basement isn't usually required unless you have need for the space. Maybe I'm assuming too much; you do have a basement? So it seems that something got lost in translation.

A house without a basement in New England would be an exception, not the rule. Going outside the rule to be an exception will always be more money than doing the norm. Plus, pier and beam in a cold climate is just not a smart choice for a kitchen ever.

I'd really question the credentials of anyone that's suggested that. It's the same as suggesting a full basement in FL where the water table is at 7'. Whaaat? Where'd you go to school? Is the more appropriate response.