The theory is also developed further in two papers by Borceux, Quinteiro and Rosický: *Enriched accessible categories* [MR1419612][1] and *A theory of enriched sketches* [MR1624638][2]. In the second one they say that they are particularly interested in case $\mathcal{V} = \text{Cat}$ and that they "intend to study this in a further publication", but I don't know of such a publication.


  [1]: http://www.ams.org/mathscinet-getitem?mr=1419612
  [2]: http://www.ams.org/mathscinet-getitem?mr=1624638