Predicting product of a Hofmann elimination with a cyclic amine

Question

What is the final product of this reaction?

Here's what I have:

Does this look correct? I'm concerned because I'm used to seeing the nitrogen removed from the product (in the cases of primary amines).

Answer 1

With excess of methylamine, I wouldn't exclude additional methylation, yielding a trimethylanilinium iodide.

However, the reaction should stop there since a further hydrogen abstraction from a $\beta$-position isn't possible.