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seek out a local independent shop that specializes in or does a lot of work on the vehicle make/model under consideration.
ask them if they'll do a "pre-buy inspection" of the vehicle for you, and at what price.
be clear that you are not asking them to make the "purchase decision" on the vehicle, but merely seeking their knowledgeable assessment/working familiarity with the vehicle so that you can be advised of the current condition and make your own informed purchase decision.
I've not had good results with the "mobile places". Have had a lot of razzle-dazzle "200 point" checklist that was all fluff and they missed the mechanical faults of the cars that were obvious to a trained/familiar with the car tech.
all the reputable dealers I've dealt with have always allowed me to do or have a pre-buy inspection.
Extended warranty? if it's the manufacturer's warranty that can be extended, it may be worth considering ... depending upon the car/price point. If it's an aftermarket warranty and you've done your due diligence prior to the purchase, it's highly unlikely that you'll be ahead with that warranty; most of them that were presented to me for repairs in my shop were essentially worthless to the car owner with very rare exception.