Is it legal to build an app that is built on top of another company's software?

You would have to have a freedom-to-operate study - also known as an infringement study - performed in order to determine if the IOSAndroid app is patented. If it is, then any use of that app, whether you are enhancing it or otherwise using it, would constitute infringement. If there is a patent, you may also want to have a validity study performed with respect to the patent in order to determine if that patent is valid - if it is, it is likely that you would infringe the patent, if the patent is not valid or you feel that it is not valid, you may not be infringing the patent. Consult a patent professional to have these studies performed.