There are some complex dynamics that take place when mass transfer is happening. In these systems this is via Roche Lobe overflow (1) which depending on the masses of the objects can become unstable after a large mass transfer. But going back to your original point, I guess there may be some configuration that leads to what to you are suggesting. Might be an interesting thing to model to see if it is possible!

(1) https://en.m.wikipedia.org/wiki/Roche_lobe

Interesting, thanks!

Because anything that massive getting into a binary system will certainly destabilise it.