How can I disable tax for certin users? How can I programmatically edit the cart to remove tax?

[Greg1234]

I need to disable the tax (tax rule) if user is "tax free" institution. None of the tax settings or tax group allows me to change the tax based on user group, only based on location.

The problem is, that if our user chooses New Jersey then we have to put tax on him (this is easy to do) but some institutions are exempt from tax, so I'd put an extra field into the form asking if the customer is exempt from tax. Putting field would be relatively easy, but I can't find any information about hook that can edit / remove the tax.

How can I access / edit the cart?