Summary: ``This paper is an extension of our last 1D, $\Cal N = 4$ supersymmetric SYK paper [1]. In this paper we introduced the complex linear supermultiplet (CLS), which is `usefully inequivalent' to the chiral supermultiplet. We construct three types of models based on the complex linear supermultiplet containing quartic interactions from modified CLS kinetic term, quartic interactions from 3-pt vertices integrated over the whole superspace, and $2(q - 1)$-pt interactions generated via superpotentials respectively. A strong evidence for the inevitability of dynamical bosons for 1D, $\Cal N = 4$ SYK is also presented.''