Yesterday a friend told me about a Holy Week "Eucharist" he attended. The various parts of the Mass were done out of order, according to the tastes of the participants, and the presider's prayers were shared by everyone.
The institution narrative, i.e. "Take this, all of you, and eat it...Take this, all of you, and drink from it," was done by the priest, of course.
My greatest problem with this sort of thing is that it reinforces a magical approach to the sacraments. It's as if you don't need a priest for some parts of the Mass, but you do for this particular part, because it's the part that requires magical powers. Thus the sacrament of Order is not about leadership or speaking on behalf of the body of Christ, in persona Christi capitis, as it were, but about a cultic, magical power.
Thus in all their efforts to appear "liberal" and "progressive," folks who do this sort of thing only succeed in putting their shallow sense of sacraments and church on display.