Does Y Combinator ever invest in the follow-on rounds of companies that have gone through its program? If not, why not? It would seem a logical easy place to own an even greater share of their most promising companies...
I'm sure there are probably others but ^ is alone is a very good reason not to participate in follow on rounds.
However, some of the YC partners are also angels and have made some investments in some of the YC companies in follow on rounds e.g. Priceonomics[1] & Crowdtilt[2]
There are others YC companies which the partners have also made investments in, I'm just highlighting two of them.
[1] http://techcrunch.com/2012/05/04/priceonomics-seed-round/
[2] http://techcrunch.com/2012/05/17/kickstarter-for-groups-and-...