  We present new infinite-dimensional spaces of bi-axially symmetric
asymptotically anti-de Sitter solutions to four-dimensional Vasiliev higher
spin gravity, obtained by modifications of the Ansatz used in arXiv:1107.1217,
which gave rise to a Type-D solution space. The current Ansatz is based on
internal semigroup algebras (without identity) generated by exponentials formed
out of the bi-axial symmetry generators. After having switched on the vacuum
gauge function, the resulting generalized Weyl tensor is given by a sum of
generalized Petrov type-D tensors that are Kerr-like or 2-brane-like in the
asymptotic AdS4 region, and the twistor space connection is smooth in twistor
space over finite regions of spacetime. We provide evidence for that the
linearized twistor space connection can be brought to Vasiliev gauge.
