Absolutely. You can obtain any CFI rating(s) you like, in any order. It is common for career types to get CFI, CFII, MEI in that order, but not necessary. Some examiners may not be used to seeing them done out of order, so I wouldn't do it unless you have a good reason (like an MEI job that starts in a week).

Your FIRST checkride for an instructor certificate is called your "initial", regardless of which rating you seek. Your initial has some extra requirements:
1) Fundamentals of Instruction (FOI) written test must be completed.
2) FOI's must be covered on the oral.
3) Some FSDO's require that a Fed, not a DPE, performs your initial.
4) The initial is usually harder, but this is not a formal requirement.

Once you have completed ANY instructor cert, all subsequent instructor certs are add-ons, with no FOI's or Fed required. They are usually easier too.

The regs treat CFI-Airplane (CFI), CFII, and MEI ratings equally. there's nothing that specifies any particular order.