Actually, depending upon what you'd like to do, you have several options for doing what you want provided you have enough equity in that home (another way of restating the LTV issue that Ram raised). You might consider putting that equity to work by partnering with an investor.
For example, you could work with a flipper as an equity partner (by borrowing at no more than 40% to 50% of the LTV--perhaps start off with something smaller like $5K to $10K if you're highly risk adverse) to do some quick turns on some lower income properties. If done correctly, then you'd be able to service the equity loans on the properties in MI and AZ. Plus, you'd generate enough to pay off the equity loan on the AZ property with 3 months (less if you're only talking about $10K or less) easily.
Another option might be a diversity play where you'd still borrow no more than 50% of LTV, and you'd invest part of that into real-estate and part of it into stocks/bonds/options/etc.
Keep in mind that you don't necessarily have to refinance to put your equity to work. You could also use a portion of that equity as cross-collateral to purchase real-estate, stocks, and other assets. Although you technically could use that equity to buy other stuff, I wouldn't recommend it. After all, if you were to buy assets that would make you some money, then you could use the income generated from those assets to pay off the debt and to buy other stuff. (It's that "pay yourself first" principle that many financial planners preach.)
I could go on and on about all of the options that you have, but I don't want to belabor my point. Hopefully, I didn't bore you with all of those options. This is exciting stuff (at least it is to me).
Anyway, please feel free to drop me a line.