I have heard that there are private M&G loft parties that are catered and have an open bar in New York. How can I score an invite?

If you know the right people, you would be able to secure an invite without asking here.  If not, you are out of luck.  Sorry, but private means private.  

Look to the thread below, re: NY mixer.  These affairs are more open, but you will need to pass screening in order to attend.  You have reviews, so you should know the ropes by now...

And the TER M & G might, repeat MIGHT p[rovide you with entre to other PP's.

Usually, smaller scale PP's are provider driven.
They invite well known and well regarded custies to meet their provider friends and vice versa.
Generally, they are not the sort of thing where you cann seek out an invitation. Rather you get invited or have to come with someone who is on the Guest List. That's how I got in to my first PP out in L.A.

This is one of those things where if you have to ask there is no point in explaining

Lina