convert M into a L visa

Hi.
I've been granted a 2 entries M back home ,and got it extended once my 2 entries expired in shenzhen PSB .
they gave me 30 days more plus 1 entry which means in total 60 days after the extension.
Do you think i can apply now for a L ,just to get one more month ,time for me to get my license employement + duty invitation letter since i got a job offer?
if no do you think once i get these documents I can apply for a Z in Singapore instead of going back to my home country (flight ticket very expensive now) ?

Thanks