  We present new steady Euler solutions on the (round) 3-sphere, that bifurcate
from an ansatz proposed by Khesin, Kuksin and Peralta-Salas, showing that these
previously known solutions are not isolated. We also extend this ansatz to any
Sasakian 3-manifold, such as the Heisenberg group and $SL(2, \mathbb{R})$.
