Can I structure a deal so the seller keeps the accounts receivable but I take the rest?

Yes, this is a common carve-out in an asset purchase. Accounts receivable can simply be excluded from the assets you're buying, leaving the seller responsible for collecting what customers owe the business as of closing, while you take on the equipment, inventory, contracts, and other assets you actually want.

The nuance is in the mechanics of collection once the business has changed hands. Customers will keep paying invoices to "the business" as they know it, which after closing is you — so the purchase agreement needs to clearly address how payments on excluded receivables get identified, forwarded to the seller, and reconciled, rather than assuming it will sort itself out informally. Some deals instead have the buyer collect the receivables as an agent for the seller for a defined period, which can be simpler operationally even though the receivables themselves stay excluded from the sale.

Because ambiguity here tends to create exactly the kind of post-closing friction and disputes that purchase agreements are meant to avoid, it's worth having a business lawyer draft specific mechanics for identifying, collecting, and remitting excluded receivables rather than leaving it as a general carve-out line.