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It all depends on your Debt To Income(DTI) and Loan To Value(LTV) ratios. If either of those don't work in any of their tables after rolling over the negative equity, you'll be denied. For example, if the lender's acceptable DTI max is 40% and the additional $6k would up the payment enough to push it to 41%, that's probably a denial. Same thing with LTV. If a lender will approve up to 120%, a $20k car would allow for a $4k buffer, a $30k car will allow for $6k. Buying a $30k car would allow you to roll over the $6k while a $20k car would require an additional $2k down to be approved, BUT, if it forces your DTI over their acceptable limit, it'll be denied.
You can always recon. If your DTI is just over their acceptable limit, but you're paying off a loan in a month or two which would bring your DTI down, they may approve it. As for LTV, most lenders will only approve around the 80% mark. Credit unions and predatory lenders will usually max out at 110%