Join as many as you want.

However, remember that any mileage-earning activity (be that: taking a flight; spending on credit card attached to a mileage account; or any other activity that has the potential to earn miles) can only be used to "top up" one of your multiple accounts. You can't take a single flight, and expect to earn miles for that flight in multiple frequent flyer accounts simultaneously.

Now, consider a scenario where you have a variable number of buckets (each representing one of the various frequent flyer programmes you have joined) but only a single hose (representing the actual "mileage earning" activities you perform - be that from flying, from credit card spend, or whatever else).

The more buckets you attempt to fill, the longer it's going to take you to fill any individual bucket (representing getting a balance in any individual frequent flyer programme where you can do something useful with those miles, or reaching a threshold where you gain status with that airline (and its alliance partners)). Even worse - some of those buckets have leaks (representing: miles might expire either through lack of activity on the account, or because miles in that programme only have a limited lifetime).

The more you can focus on a particular airline - or a particular alliance - and the more you can focus on a particular frequent flyer programme - the quicker you can fill a single bucket, and the more useful that bucket - and the miles it contains - will be for you.