Yes, they COULD........however: If a person is arrested for a traffic offense and agrees to submit to a breath test (and they take the test), that it it. You cannot then turn around and ask for blood unless you can articulate why you suspect drugs are involved OR you are able to get a search warrant. And of course this is assuming that the breath test given at the scene is an actual breathanalysis test and not just a PBT. If you give a PBT at the scene of a major collision and it supports your PC that the driver is drunk, you had best be going for blood as opposed to a breath test for alcohol.