Great idea. India sort of allows something like this. They have a program called Overseas Citizen of India (OCI) which allows one to become a citizen of India without denouncing the citizenship of another country. Currently they only accept people who were previously Indian citizens (or are children of such). But if they relaxed these rules it would be similar to what you described.
http://www.immihelp.com/nri/overseascitizenshipindia/oci-eligibility.html