i.e. If there is asbestos in my flooring and asbestos around my water pipes, can one contractor remove both? Or do I need a flooring contractor who specializes in asbestos removal for the flooring part and an insulation contractor for the other?
It depends on the state you live in. Every state will have their own regulations regarding the remediation of these materials and sometimes the states will break it down to the county level. What I would suggest is finding out your official website of the state you live in. From there you should be able to find the answer to your question but if not just give them a call and they will be able to answer your question.
As long as the removal does not involve structural demolition, than YES one asbestos abatement contractor can remove from you site.