  In this work we present novel and known three-dimensional hypergravity
theories which are obtained by applying the powerful semigroup expansion
method. We show that the expansion procedure considered here yields a
consistent way of coupling different three-dimensional Chern-Simons gravity
theories with massless spin-$\frac{5}{2}$ gauge fields. First, by expanding the
$\mathfrak{osp}\left(1|4\right)$ superalgebra with a particular semigroup a
generalized hyper-Poincar\'e algebra is found. Interestingly, the
hyper-Poincar\'e and hyper-Maxwell algebras appear as subalgebras of this
generalized hypersymmetry algebra. Then, we show that the generalized
hyper-Poincar\'e CS gravity action can be written as a sum of diverse
hypergravity CS Lagrangians. We extend our study to a generalized hyper-AdS
gravity theory by considering a different semigroup. Both generalized
hyperalgebras are then found to be related through an In\"on\"u-Wigner
contraction which can be seen as a generalization of the existing vanishing
cosmological constant limit between the hyper-AdS and hyper-Poincar\'e gravity
theories.
