There is little overlap in a BSEE with a BSME; and so the time investment would be tremendous. Instead, focus on a specialization within EE that you find fascinating. I am getting my MSEE in semiconductor devices and solid states to complement my BSME. It's often been said to get a management degree, but save that bullet for when your already working in a company (if that's your decision); else it won't bridge as far you think. In a realistic standpoint, get a JD... you'll travel farther than a MBA student will. Use the legal knowledge as means to make sound business decisions and not go the average IP route.