To answer this question, you must first look at why someone would even want to do this.
All societies are not equal: for example, some societies in Europe (such as GEMA and SACEM) give pensions to its songwriter members provided they have reached a reasonable level of income over a 10-year period. Others, such as the PRS in the UK do not. In the US, there are also no pensions at BMI, ASCAP or SESAC but there are wide variations in the way they distribute the money they receive on behalf of songwriters and publishers.
It is very difficult - but not impossible - to be a member of more than one society. If you are extremely successful and therefore a very high-earner, you have the power to (for example) let BMI collect North American royalties whilst SACEM collects the rest of the World (paying you a pension too !). But you have to know the right people to make this happen. If you contact your local society they will probably say it cannot be done.