Is there one legal system that could cater for all cultures around the world?

All the humane be share same adherence to moral level which is more general  than legal practices. So the answer is yes the natural law is the law of all cultures and the moral practices judges these behaviors     

I believe that each legal system is very different however, those that originated from religion could have a similar basis. Additionally, they have all been altered to suit changing times. The way that each legal system is run is also different and this is why you will find that there are corrupt systems that are not protected by a rules governing the law preventing corruption. I believe that we can learn from different legal systems combining laws to create an international system that guides states to improve their own systems of laws. What do you think?

Sadly just as the world does not share a common language it does not share a common law. The basis of law in countries around the world will often be contained within the various customs, practices, religious beliefs and political systems that are embraced by each country. The laws of some countries have a basis on those of others. The laws of the USA have some foundation in English Law although the constitutions of the USA and the UK are founded on different principles. In the USA they have a constitution that is written and codified and in the UK its constitution is mainly based upon common law and custom. Even within the geographical bounds of a country the laws can be based upon different precepts. For instance within the UK Scottish Law is predominantly based on Canon or Roman Law and English Law is based upon Common Law. There are conventions that apply internationally and are accepted as general principles such as the INCOTERMS that apply to methods of shipment of goods, the Treaty of Rome that is applied across Europe and the Convention on International Contracts, although with the latter some countries refuse certain aspects of the Convention because it allows "oral contracts" to be binding. In conclusion alas there is no single, binding law that governs all of us.

well, i think that most of global legal systems are similar in their essential principles , for this legal systems in many countries seem familiar in their provisions , such as a terms that govern civil actions and principles of contracts in general . while cultures affect in some details or impose a limited legal forms