You're putting tobacco into the pipe with it still burning?

I'm no expert by any means. I'm still a newbie to pipes but it doesn't sound like a good idea.
If you have a nice, or even an average briar pipe it is best to smoke it all the way down and sit it aside for 24-48 hours.

If you want to smoke more often than that, get you a corn cob pipe or two from Walgreens. They're only $5-$6 each and they smoke great.
I've been known to smoke 2-3 bowls back to back in a cob. If they burn out who cares, they're cheap.

I wouldn't do it with a briar though.