Sorry, maybe in my previous post it was not clear but the deadline I was talking about is the one to apply to Japanese universities (to send the documents and ask for a LoA). The deadline for my embassy is the 12th of September and both the universities know about it, I also asked them for a scan of the LoA in case the hard copy might arrive late.
However, if they give me a negative answer after the 31, I won't be able to apply for other LoAs...
Of these two universities, I contacted one around 20 of August and the other one around the 5th. Maybe it's ok if I contact again the second university because it's been 3 weeks since the last contact.
So do you think it is better not to mention that I'm planning to apply elsewhere? Unfortunately, I think that if I don't mention that, it might be difficult to come with an excuse for asking for an unofficial answer withing the 31th, because they already gave me all the info: at the beginning of the month they told me the LoA would have been sent around 1-10 of September and I replied it was ok as long as they send the scan copy within the 12th of September X(
I don't know how to ask without mentioning the other universities
But are we allowed to ask for more than three LoAs at the same time? In that case I would send documents to another university right away since I already have a professor which approved my project X(