Sign the first offer, continue interviewing, if you end up switching companies just write a nice email to your recruiter/manager explaining the situation. It wouldn’t be the first or last time that it’s happened.
replyIANAL, the above isn’t legal advice, yada yada.
If they refuse to give you more time (they often will, if you demand it) then just accept the offer and keep interviewing during the interim before your start date.
replyI'd be cautious of this strategy, reneging has consequences both for the company that you ditch and the company that you eventually sign with
replyWe pulled an offer we made because one of our candidates apparently had already accepted an earlier offer from another startup.