  This article introduces two new constructions at the higher homotopy level in
the space of Legendrian embeddings in $(\mathbb{R}^3,
\xi_{\operatorname{std}})$. We first introduce the parametric Legendrian
satellite construction, showing that the satellite operation works for
parametric families of Legendrian embeddings. This yields new invariants at the
higher-order homotopy level.
  We then introduce the parametric connected-sum construction. This operation
takes as inputs two $n$-spheres based at Legendrian embeddings $K_1$ and $K_2$,
respectively, and produces a new $n$-sphere based at $K_1\# K_2$. As a main
application we construct new infinite families of loops of Legendrian
embeddings with non-trivial LCH monodromy invariant.
