B-2 extension for F-1 Request


I'm currently in the US on a B-2 visa, came to visit friends and relatives.
During my stay I decided that I would like to attend to a certain college.

I entered the US On the 4th of April, which means my current status is valid only until the 3rd of October, About a month from now.

Because I need to maintain my B-2 Status while waiting for a F-1 approval, I have to submit an I-539 form twice,
One as a B-2 extension request and the second one as a F-1 change request.

I have yet to submit any of those because I'm waiting for an I-20 form to be issued by the college and I'm really running out of time as any day goes by..

Should I send the extension request now, before receiving the i-20 form, and mention that the request is filled so I can maintain my B-2 status and that the F-1 request will be sent in the following days? or should I wait and send the both of them together?

I'm supposed to get the i-20 form in about a week or so, which means I'll have about 20 days before my current I-94 expires..
And I don't think that this is a good situation..

Thanks in advance!