I have found several sites which mention how a flower stops it's own pollen
from fertilizing it, but none mention if this same flower can accept pollen
from a compatible plant while holding back it's own pollen.

In other words, if pollinated with it's own pollen, will the bloom die, or
is it still accepting of a 2nd pollen? Solanaceae is the family in question,
Brugmansia specifically.

Rumor has it that the breeding potential of the bloom is ruined if self
pollinated, and yet the pistil is often located among or behind the pollen
bearing anthers, which is a very poor design if this is the case. I don't
think nature would be so careless, but .....?