I have heard of families descended from up to 8 convicts but these were rare
I'm extremeley lucky, being one of those rare direct blood descendants of 8 convicts;
1) Sarah Dorset "Lady Julianna" (2nd Fleet) 1789
2) Mary Harrison "Mary Ann" (2nd/3rd Fleet - debatable) 1791
3) Edward Robinson "Admiral Barrington: (3rd Fleet) 1791
4) George Smith "Fortune" 1806
5) Mary Clark "Woodman" 1823
6) Wlliam McCready ""Recovery" 1823
7) Thomas Sarjeant "Maquis of Hastings" 1827

Stephen Williams "Eleanor" 1831
plus quite a few more who married into the family of direct blood ancestors. Also, lucky enough to have Robert Watson, a 1st Fleet crewman abaord the "Sirius".
Though in seeing Di's response of having 17 convict descendants, she is certainly a rarity!
Family Trees are an amazing thing. I compare my convict ancestors with other ancestors on the same family tree level. Some of these include Sirs, Countesses, Reverends, high ranking military men, and extremely wealthy businessmen. Its an incredible comparison, but I would never swap any of them - rich/poor or gentry/convict!
Les
Les