I did my CFII and MEI at the same time.... I trained in a Duchess while getting my 15 hrs PIC and as soon as I got them I went to the checkride where the DE didn't want to do both checkrides in the same airplane so we jumped in the Duchess and did the MEI portion and then went on a C172 and finished the CFII. I would highly recommend it, it does take more work and you will need to prep more but it is doable and it pays off at the end. Make sure you call the DE in advance and let him know of your thoughts and to make sure that he can do both checkrides because some DEs can't do MEI checkrides and some can. Best of luck.