So I unfortunately can't link you to a particular document that says two loans are hard for subprime. I'm sure if you made friends with someone in the finance department of a dealership they could show you some approval guidelines though...I know through third-hand experience + asking/making friends with people in the finance department of auto dealers.
I will also say that it's not impossible for subprimes to have more than one open auto note. With a good story, and if everything else falls into place as you mentioned (DTI, dp, LTV), it can happen. But I'm willing to bet that if the OP went out and tried right now without trading in his current note and with no co-signer, he'd encounter pushback/difficulty. In fact there's countless stories/threads of that exact situation on our forum and others.
Why you ask when everything else would seem like the loan should be approved? I can tell you the rational reasons why lenders hesitate. And by the way, a prime customer will run into the same thing if they try to get 3+ (or 4+ depending onlender) open auto loans even if everything else is fine.
Situation 1: Subprime customer with one open loan buys another auto. Well backstory (that he doesn't tell the finance company): his old car was failing and it has so much negative equity, there's no way to trade it in. Soon after new car's loan closes, customer defaults on old loan. Lowers the fico of customer + this means that customer now has people chasing him for the deficiency. This is especially terrible for the finance company if your old loan is also with them. For this reason, the same company will almost NEVER write two simultaneous loans for a subprime customer.
Situation 2: Subprime customer buys the other auto for someone in his family. That's nice and all, but let's say this other person doesn't co-sign. If the driver stops giving our borrower the monthly payment or our borrower hits financial trouble, he will stop paying the second car. Because he doesn't need it everyday, the consequences of a repo serve as less of a deterrent to not paying.
Situation 3: Subprime customer buys 2 autos for himself. If he gets into any financial trouble, the second car loan payment is the first that's going to go unpaid...like scenario 2, he doesn't need 2 cars and a repo won't effect him quite as much as if he only had one primary car to do everything.
