There is no rule saying you can only have one car loan. However, your credit and income may not be sufficient for the second car loan.
In any case, it is a very bad idea to co-sign or lend your credit to anyone you are not legally married to. Not matter how confident you are and trusting, it is very likely going to turn out bad. Besides the potential credit damage if they pay late or default, your name would also be on the title to the car. You would then be held equally responsible for proper insurance and registration. You could lose your driver's license over lack of insurance, expired tags, or parking tickets.
Further, if she has an accident in that car, you could be sued for damages.
Let your friend do without a car or look for a cheaper one.