We discuss the conditions for extra supersymmetry of the N=(2,2) supersymmetric vector multiplets described in arXiv:0705.3201 [hep-th] and in arXiv:0808.1535 [hep-th]. We find (4,4) supersymmetry for the semichiral vector multiplet but not for the Large Vector Multiplet.
@article{arxiv.1008.3186,
title = {Off-shell N=(4,4) supersymmetry for new (2,2) vector multiplets},
author = {M. Goteman and U. Lindstrom and M. Rocek and I. Ryb},
journal= {arXiv preprint arXiv:1008.3186},
year = {2011}
}