  We classify all compact simply connected biquotients of the form $G/\!\!/
SU(2)^2$ for $G =SU(4), SO(7), Spin(7)$, or $G = \mathbf{G}_2\times SU(2)$. In
particular, we show there are precisely $2$ inhomogeneous reduced biquotients
in the first and last case, and $10$ in the middle cases.
