Can a buyer insist certain contracts be excluded from what they're taking on?

Yes — in an asset purchase, this is one of the most routine points of negotiation, not an exception. The purchase agreement typically includes a schedule identifying exactly which contracts the buyer is assuming; anything not on that list simply isn't part of the deal, and the obligations under it stay with the selling corporation.

The nuance is that excluding a contract on paper doesn't always solve the practical problem behind wanting to exclude it. If the contract covers a customer, supplier, or lease relationship the business genuinely depends on to keep operating, leaving it out may mean the buyer needs to negotiate a fresh agreement with that same counterparty directly, on new terms, rather than truly walking away from the relationship. And for contracts you do want, some — commercial leases in particular — require the other party's consent to assign, which isn't automatic just because it's listed as assumed.

Deciding which contracts to take, which to leave, and which need separate handling is a core part of structuring an asset purchase agreement properly. A business lawyer reviewing the seller's material contracts before the schedule is finalized is what keeps this from becoming a post-closing surprise.