In the report, The Royal College of Midwives estimated that the odds of these consecutive sets of twins at such a young age were more than 700,000-to-one, noting that it is more common when multiple pregnancies are separated by singletons.

Examples 

While the circumstances are very rare, there are numerous incidences of families with multiple multiples. Although some are related to reproductive assistance, many are completely spontaneous. For example, Kevin and Lorraine Horan of Ireland, have three sets of twins and never used any fertility treatment. And this article references two families whose second set of twins were complete surprises. Sometimes the multiples are a result of fertility treatments; Fran Pitre details the story of her three sets of twins in her book Twins X3.

Odds of Having Another Set of Multiples

After having a set of twins, is it more likely that a woman will have another set? It is thought that the odds increase for a mother who has already conceived and carried twins. Both hereditary and environmental factors may contribute to this. Mothers who conceived dizygotic twins due to hyperovulation are already more likely to have twins. After carrying a twin pregnancy already, their womb is more likely to successfully sustain subsequent multiple ​pregnancies. The Guinness Book of World Records attributes the following women as mothers with the most sets of twins:

A Russian peasant wife, whose name is not known, gave birth to 16 sets of twins before her death in 1770. She was the first wife of Feodor Vasilyev. Barbara Zulu of Barberton, South Africa had six sets of twins in a seven-year period in the late twentieth century. Three sets were girls and three were boy/girl twins.  Even though she was from Johannesburg, South Africa, Anna Steynvaait gave birth to true Irish twins—two sets of twins within 10 months in 1960.