
I think 11 weeks is extremely young to expect your pup to be clean throughout the night .
As long as he is let outside before bedtime and given treats as you say for "doing his business" he will eventually get the message . If he is clean during the day then he is doing very well for his age .
What time do you rise in the morning and go to see him ?
Maybe you could get up either in the night to let him out ( which isnt very practical especially if you work) or get up slightly earlier to let him out .
With perseverance and patience he will get there but as i say he is VERY young to expect total clean day and night .
Lel