Can I have two MileagePlus Explorer Cards simultaneously?

When I registered for United's loyalty program years ago, I chose the title of "Baron". United has occasionally confused this title for my first name in various places throughout their system, including tickets.

I am currently a United MileagePlus Explorer card holder. I recently received an offer to apply in the mail, addressed to "Baro X Y" where X is my middle and Y my last name.

Can I apply for another card with the same address and social security number? I wouldn't mind another 50,000 miles.

Thanks,

Baron