Having the option to receive text/sms notifications rather than emails would add convenience and facilitate more timely interaction between sellers and buyers.
Giving the user the ability to control notifications on individual message chains, users or for certain scenarios, like new inquires may be beneficial.
This could potentially be a premium member benefit if needed.
Welcome, and I’m not sure but summoning our people that would know about this… Well much more than me at least. Lol
Edit*
@eaglereptiles @john @Lumpy @t_h_wyman
We’re always looking at ways to notify members of any messages they receive. We understand that email isn’t the main communication tool for the majority of people.
However note that we will always be improving MorphMarket Messenger so this will be the best method to communicate.
I’m not sure on the Sms part as that seems like it could be a costly service to maintain with very little ratio in regards to interaction.
Push notifications however would make much more sense and allow us much more freedom to customise which notices we want to see as users.
This doesn’t seem too far off from now 
Yes the primary way we intend to address this is with the upcoming app release, which will include notifications right to your home screen on your phone. We’d like to see how that does before SMS (which is expensive, but yes could be a prem feature).
Yes push notifications would be great similar to messenger 