Yes, you are legally and operationally permitted to be a member of as many frequent flyer programs as you wish. In fact, most savvy travelers belong to at least one program in each of the three major global alliances: Star Alliance (e.g., United, Lufthansa), SkyTeam (e.g., Delta, Air France), and Oneworld (e.g., American, British Airways). However, while you can hold multiple memberships, you can usually only earn miles for a single flight in one program. You cannot "double-dip" by earning United miles and Lufthansa miles for the same seat on a codeshare flight. The best strategy is to concentrate your flying within one alliance to reach elite status faster, but maintaining accounts with different carriers allows you to take advantage of specific promotions or use partner miles for unique redemptions. Just be mindful of "account dormancy"; some programs will expire your miles if there is no activity for 12 to 24 months, so it is better to have a few active accounts than dozens of empty ones.