I assume you know this, but just to mention it:

For issuing cards, you can use Stripe nowadays. If you're doing this as part of your business (e.g. like Expensify is doing), its available to all US based businesses: https://stripe.com/issuing

The more convenient Stripe Corporate Card (which sounds like that may be your use case?) is still invite only: https://stripe.com/docs/corporate-card

(I myself am queued up for an invite on the Corporate Card, and using Chase Credit Cards in the meantime, which are okay, but not great)