Categorical Multi-Combinators form a rewriting system developed with the aim of providing efficient implementations of lazy functional languages. The core of the system of Categorical Multi-Combinators consists of only four rewriting laws with a very low pattern-matching complexity. This system allows the equivalent of several -reductions to be performed at once, as functions form frames with all their arguments. Although this feature is convenient for most cases of function application it does not allow partially parameterised functions to fetch arguments. This paper presents Partial Categorical Multi-Combinators, a new rewriting system, which removes this drawback.