OP, this is where you are confused.
It's seems you have a METV.
There is no "triple entry" about it.
To maximize the stay in Thailand with this visa you would exit and reenter just prior to expiry.
That would stamp you in for another 60 days.
To exit Thailand after that you would need a reentry permit.
In your case that would be done prior to May 12.
In all that visa can provide almost 9 month stay.