We don’t normally have fellowship at Mass, since Mass is about worship, but my friends from Church and I do all sorts of things at the Church together,
outside of Mass times.
Catholic Churches are available all day long from early morning until quite late at night, and you can book the space to have pretty much any kind of meetings (obviously, nothing that would go against the Faith, but as far as Bible study, or Women’s League, or Rosary prayer group, etc.) , as long as it’s members of the parish who are organizing the meeting, as long as everyone is welcome to attend who wants to attend, and as long as someone has a key to lock up afterwards - it’s kind of like a community centre, in that sense, and, at least at my parish, there is always
something going on somewhere in the building - maybe not in the Church itself, but in the Hall, or in the meeting rooms of the Rectory, etc. - the place is jumping all the time, and as I mentioned above, everyone is welcome to participate in everything that’s happening.
Our Pastor even throws karaoke parties in the Parish Hall quite frequently, with pig roasts, and everything (he’s a missionary to Canada from the Philippines) - it’s
great fun!!