The short answer is that you'll need to take the written and practical test for any FAA license you wish to obtain, assuming you meet the experience requirements. Be sure to bring documentation of such to your checkride, including Mexican charts to demonstrate cross-country requirements are met.
If you are not a US citizen, you'll need to go through the TSA process (
www.flightschoolcandidates.gov) before you can begin training in the US for your instrument and multi-engine checkrides.
Is your FAA private on the basis of an FAA practical test or your foreign certificate? If the latter, be sure to backfill any unfufilled experience and training requirements for that rating before taking your IR/Commercial checkride.
I am not familiar with handling foreign type ratings; one of the big US training facilities for such could better handle those questions.
I don't recall there being any agreements in place to specifically ease the conversion from Mexican licenses to FAA, but I primarilly work with people who have JAA certificates. As Douglas recommended, taking a look through the FAA website may help.