  We study a class of arrangements of lines with multiplicities on the plane
which admit the Chalykh-Veselov Baker-Akhiezer function. These arrangements are
obtained by adding multiplicity one lines in an invariant way to any dihedral
arrangement with invariant multiplicities. We describe all the Baker-Akhiezer
arrangements when at most one line has multiplicity higher than 1. We study
associated algebras of quasi-invariants which are isomorphic to the commutative
algebras of quantum integrals for the generalized Calogero-Moser operators. We
compute the Hilbert series of these algebras and we conclude that the algebras
are Gorenstein. We also show that there are no other arrangements with
Gorenstein algebras of quasi-invariants when at most one line has multiplicity
bigger than 1.
