Multiple University Recommendations

Is it possible to be apply to two different universities and receive a MEXT recommendations for both? I am applying to be a research student and received provisional supervision from two research labs and was wondering if I would have to choose one or could apply to both. Additionally, if I do have to choose one is there a way to research which university/professor would give me a better recommendation?

if you don't decide it at first, how they can choose you in the next step ?

each university has a limited (small ) number of scholarship positions. they don't want to waste their valuable positions by your double applications.
when you make double applications, probably, each university and MEXT will get angry for you.
as a natural result, your MEXT scholarship will be surely denied and, in the worst scenario both university may cancel the acceptances, because of your dishonesty. honesty is highly important in Japan. (maybe not in your country)