There is no proper distinction between the visible Catholic Church and some invisible Church which contains more people. Frankly, that distinction is total Protestantism.
Membership by desire in the Church is invisble/informal communion with the visible Church.
Sir, if you read my post # 156 I did not use the term "invisible Church." I am very well aware that it is a Protestant idea. That's why I did not use it. I did, however, use the language of Lumen Gentium as well as the language of Piux IX and others--that the total Church of Christ subsists in the Catholic Church, that is, the visible Church consisting in those bishops and their flocks who are in communion with the Bishop of Rome, but that others (your baptism of desire) can be saved and if they are saved they are saved through the Church of Christ that subsists in the visible Catholic Church but that one need not be a formal adherent of this visible Church to be saved.
I wish you would not accuse me of using language I did not, deliberately did not, employ. Your quarrel is with John Paul II, e.g., in Crossing the Threshold of Hope, with Lumen Gentium, with Piux IX.