There's certainly a heritable component - some breeds are very likely to have multiple births (eg., Leicesters, Mules, Lleyns) and some very unlikely (eg., Herdwicks) - although nurture is a very important component too. (We don't flush our ewes as we like to have plenty of good strong singles; in years when the climate flushes them for us
we get loads of twins...)
The multiplicity complex must come down the male line too - the Mule is fathered by the Leicester; she doesn't get her tendency to triplets from her Blackfaced / Swaledale mother.