If they are high maintenance, my inclination would be to say no. However, because I'm not an expert at cleaning up dead bodies, I'd ask your local crime scene clean up company what their opinion was. If you can't find them, call the police and ask who they use. It's usually a private company that comes in and cleans up all the gore for a fee.
I'm of the notion that this is a business and I'm more than happy to try to make my customers happy, but if they are high maintenance, at some point, you're going to have to be the "bad guy" and say no.
For example, I've got a tenant who is ALWAYS late with the rent. She pays the late fees no problems, but my property manager is constantly having to chase her down for the rent. On top of that, she's had nothing but excuses and has lied about where the rent was (rent was in the mail on the 10th she claims, but envelope is not stamped until the 13th)
She actually had the nerve to come to me and ask for a complete bathroom remodel. Nevermind that there's nothing wrong with the bathroom, she just wanted a jetted tub, tile floors, and a new vanity she saw at home depot. All told, it was north of $5,000 just in parts. I told my property manager to tell her flat out no. That was almost an entire year's worth of profits for that property. On top of THAT amount of nerve from her, then she had the nerve to say she'd go in half's with me.
My thought was: "Well, if you can afford half of the bathroom remodel, why can't you pay your rent?" and "If she bails on me, I'll be on the hook for the entire amount".
High maintenance people are a pain, but just do your research with a crime scene clean up company and their opinion, and be firm if the answer is no.