Not vehicles, so I may be off, but we hate starting to negotiate price with a customer when we pretty much know that they are using us as the “first stop” jump off point to leverage against the next shop. We have to do our best to find out if the customer is curious, serious or using us.
That said, try the straight up approach. If you are going to shop them, let your first stop know that you are serious about making this purchase but have to check other places for price. *If you like the service you got at the first place*, let them know that you will give them the last shot to match the lowest price you find, and stick by it. So many customers will get the bulk of their help from their first contact and then give the commission to the place they get shoppers fatigue at, often even at the same price.
Sales is a tough gig. Take care of the folks who earn your business.