Hi Monica - welcome to the vaccine support board...
This question comes up often on this board. There are several things to consider...
(1) Merck produces the monovalent vaccines but, I believe, measles and/or mumps is not being produced right now and rubella is on backorder. You can contact Merck at 1-800-MERCK-90 (1-800-637-2590) or 1-800-NSC-MERCK between 8 a.m.–7 p.m. (ET) Monday through Friday to inquire specifically.
(2) There is no evidence that monovalent M-M-R vaccines are somehow "different" or "safer" than the trivalent MMR vaccine. There is more info about this at the "MMR The Facts" website in the UK specifically looking at single vs triple vaccine: http://www.mmrthefacts.nhs.uk/library/single.php
(3) There are other risks associated with monovalent vaccines. By getting 3 separate shots, there is more than double the fillers/adjuvants being given. Statistically speaking, your risks of driving to the doctor's office 3 times and being in a severe car accident is higher than the risks of severe adverse outcome from a single MMR vaccine. There's also the risk of actually contracting the measles, mumps, and rubella but this is probably small given that others have vaccinated their children for MMR and provide community immunity.
My children have received the MMR vaccines (twice for DD and once for DS) according to the currently recommended vaccination schedule. There are other people on this board who have chosen to delay MMR....they might give you some insight into doing this.
HTH - Eve - Vaccine Support community leader