Yes, a company can be set up to pay on account, so its staff book without entering a card at all. Instead of each traveller paying at the time, every booking is charged to that company's account on your portal, and you send one invoice or statement covering the period you have agreed with them.
Once that account exists, the booking screen behaves differently for those travellers. They search and book as normal, and at the payment step the cost goes to the company account rather than asking for card details. Each booking is stamped with the traveller, the department and any reference the company wants to see on its invoice, such as a cost centre or a project name, so when the statement goes out the company can tell what every line was for. You can also set a credit limit on the account, and bookings stop once it is reached, which protects you if the company falls behind on payment.
Be honest with yourself about who is carrying the money in the meantime, because it is you. Some suppliers take payment from you the moment a booking is made, so you are funding those trips until the company settles, and how far you can avoid that depends on your own arrangements with the airline or hotel supplier rather than on the portal. Whether pay on account is available to you in the first place can also depend on your plan.
Before you offer it to a client, decide the credit limit and the payment terms you are comfortable with, and check which of your suppliers charge you at the moment of booking.