Over 50 years I have now caved with four generations of the same family.

I have caved with 4 generations of my own family, but only 3 at any one time 

Me too, though Granny couldn't be enticed very far into Goatchurch or Denny's Hole and absolutely refused to consider Swildons. She felt Aveline's Hole had about the right combination of moderate darkness and minimal discomfort together with sufficient space for an underground picnic.

I too can only manage 3 generations. Grandson Harry is now 14. If he produces offspring when he is 18 I will 75 then so I may just make it to 4. If he lets me take his 1 year old underground 

OR doesn't mean at the same time. Only ever managed 3 generations underground at same time but OR has now caved with my father, me, my daughters and one of my granddaughters who so far, aged 5 has made a trip to the lake in Prid and explored Hilliers Cave. You won't see photos of her on social media because my daughter has embargoed them.

I have been underground with my grandmother (77 at the time and a former Mendip caver) and my eldest son on one occasion, but we were missing my mothers generation for that trip.

My mother never really got the caving bug (though her brother did for a short while), but I've managed to get her into a few places with the kids. Not really proper caving though.

Here is the youngest generation in The Drainpipe at the weekend:

I think the only cave we ever got my mother into was W/L and that was about the first 20 metres with her saying every step "Can we go out now?".  She used to stay at home and worry when we went off caving. If you dig around you will find a letter she wrote to the Speleologist mag. in 60's. They got her name wrong and used her address (it happened to be Jocelyn Mews) much to the hilarity of my caving companions who still remind me about it to this day.

My mother was similarly under-motivated.... She used to come along on fairly straightforward trips to make sure my father wasn't using me to probe very narrow passages impassable to normal adults (this was long before I grew body hair or shoulders) but eventually the psychological distress caused by going caving became greater than the anxiety caused by letting us go unsupervised. Paradoxically, she was greatly reassured when we started caving with Howard Kenney, who was much more likely to encourage the exploration of very tight passages.

Never managed to get all three generations at once, but my father postponed his first cave till he was 86. We took him into Yordas main chamber, and then into Old Ing, but he got a bit frail after that.