It's not just a matter of X or X & Y. It's all about one's credit profile and that activity and whether or not the activity is seen as too much of a risk for a given creditor. Person A could attempt what you're looking to do and get denied for both. Person B could only get approved for one. Person C could get both with not so great terms. Person D could get both with best possible terms. It's all about what an individual's credit profile qualifies for versus the creditor/product's underwriting criteria.
We really can't tell you for certain based solely on a score if you'll have problems doing both. 700 is generally good but creditors don't all have identical underwriting criteria or risk tolerance. Definitely order the actions based on priority in case your creditors don't support both. If I had to guess I don't think you'd have trouble with both though you might not get best possible terms on both. However, it's never just about score and i'm not an underwriter for your creditor's auto loans.
