I don't believe you can do this with Shopify Payments (Stripe based). There may be other payment gateways that will allow you to disburse funds to multiple accounts, though.
Our group would also like the ability to have funds go to different accounts. We are a community group that sells flowers and tickets to special events - funds go to one bank account, we collect donations - funds go to a second bank account, and we collect dues -- funds go to a third bank account. Is it possible to link these 3 accounts to different pages on our website that is hosted by Shopify?