You can buy property etc. with any offshore company that you register. The question may be if the person or company you buy from has any restrictions to the jurisdiction where the company is located. For instant in Turkey they will only accept companies from Turkey to buy property as far as I remember (correct me if I'm wrong) and in most part of Europe you will need to have some European company to buy property, for instant a Cyprus company. This depends at the end of the day all on the guys you buy the property from.
That all said, it's your company once you registered it and you can do exactly what you want with it. There is no one to ask.