I've got a site that serves several business units of a company. The company would like to be able to sell different products from each business unit. Each business unit has their own Authorize account and would like to process transactions using their own Authorize account.

So:

• Business Unit A would like to sell widget A, and process the transaction on Authorize account A.
• Business Unit B would like to sell widget B, and process the
  transaction on Authorize account B.
• Business Unit C would like to sell widget C, and process the
  transaction on Authorize account C.

For bookkeeping reasons, they can't share a single authorize account. The site is using WooCommerce.

I've done a fair amount of searching, and I've found plugins and methods for using multiple different gateways (e.g. Authorize and Stripe) but not multiple accounts for the same gateway, because keys tend to be per install.

I'm pretty sure the answer to the question is "no", but I want to make sure I'm not giving up prematurely.