Answer: Yes, it's fine to do this. There are really only two disadvantages. The first is the time it will take for you to fill the applications out. The second is that some insurance companies charge an application fee and almost all require that you provide a check, credit card or banking information to cover the first modal premium. This means that, if you are approved for coverage, you could end up canceling coverage with more than one company and having to wait on a refund. If you can say more about your health issues and the treatment you are receiving, your height and weight and whether or not you smoke, as well as the state you live in, I can give you more specific guidance as to which company might work best for you given your health conditions and the various underwriting guidelines. Good luck!