  We introduce several algebraic structures related to handlebody-knots,
including $G$-families of biquandles, partially multiplicative biquandles and
group decomposable biquandles. These structures can be used to color the
semiarcs in $Y$-oriented spatial trivalent graph diagrams representing
$S^1$-oriented handlebody-knots to obtain computable invariants for
handlebody-knots and handlebody-links. In the case of $G$-families of
biquandles, we enhance the counting invariant using the group $G$ to obtain a
polynomial invariant of handlebody-knots.
