This one gave me pause, but I don't think this question is grammatical.
Consider how this question would be answered:
— How much more time are you going to stay online?
— I am going to stay online for ten more minutes.
The time is not a direct complement of the verb stay, it requires a preposition.
For how much time are you going to stay online?
Contrast with a verb that doesn't take a preposition:
— How much more time are you going to spend online?
— I am going to spend ten more minutes online.
If you use “how much longer” instead of “how much more time”, then you don't need the preposition, because longer works on its own as an indication of time.
— How much longer are you going to stay online?
— I am going to stay online just a little longer.
“How much longer are you going to stay online?” is the idiomatic way of phrasing this question.