No, that's not possible. Every hotel property management systems I've ever encountered only has the ability to attach one card to a room. One way to split charges would be to physically hand your secondary card to the person charging those incidentals. Unfortunately, this has implications on the earning of Marriott Rewards points. A second option would be to go to the Front Desk when you check-out and have them charge the secondary card for those charges. But, that only works if you have enough credit left on the card. (See next paragraph.)
You may already know this, but when you use a credit card at a hotel they authorize a hold equal to the amount of the room plus a certain amount per day for incidentals. If the room/tax amount of the stay will put you close to your limit, you may run into problems at check-in. It might be worth contacting the hotel to find out how much extra they hold per day. Make sure you call the hotel directly, as this probably isn't a question that a Reservations agent will be able to answer with certainty.
Added later: After thinking about this some more, I think I found a better solution. When you arrive at the hotel, ask them to charge the full amount for room/tax onto your Marriott Visa. Then, give them your secondary credit card for incidentals. In theory, you wouldn't have any issues with holds/authorizations doing it that way. I'd still recommend reaching out to the hotel prior to arrive to confirm that they will be able to do this for you.