I actually just had this issue.
I Stage Managed Footloose back in May for a very respectable theatre company downtown. After the show closed, I was offered to Stage Manage the opener for the next season, Cats, as well as possibly the whole season. I was ecstatic and couldn't refuse this kind of opportunity, especially with the reputation of this company and the wonderful people I would get to work with.
However, at my university I am the only Stage Manager. I have always Stage Managed shows for one specific director, and she assumed that I was doing her show in the fall. It just so happened that the two shows, hers and Cats, were pretty much at the exact same time.
I really struggled with my decision, but ultimately I talked to the director at my university and explained the opportunity to her. I was open, honest and direct, and she really appreciated it. She understood and encouraged me to take Cats (which I am SO thankful for by the way) and I came out on top.
Unlike me, you have the luxury of doing both shows. I think that I would drive myself a little crazy if I tried to do two shows at once with everything else that I have to do. It's not necessarily unprofessional; however, you really need to decide if you can handle both shows and dedicate adequate attention to both. If not, then it will stress you out and you won't do your best. The musical is a great idea; however, make sure that you are able to commit to both equally. Also, make sure that the directors know that you are doing two shows. It would be unfair to them if you were not completely honest about your situation. Just as long as you are open and honest to other people and to yourself and feel like you can take on both shows in their entirety, then go for it! If not, then think about the choices and do what is best for you.