The 3° amine stabilizes the tetrahedral intermediate, making the elimination of the alkoxide group of the starting ester more likely.

An acid-base reaction occurs between the 3° amine and alcohol, forming an alkoxide ion that is a stronger nucleophile.

The 3° amine forms a complex with the carbonyl group, making it more susceptible to a nucleophilic attack from an alcohol.

Nucleophilic attack by the 3° amine forms a positively-charged amide that is more reactive than the starting ester.