On any involuted semigroup $(S,·{,}^{\text{'}})$, define the ternary operation $\left[abc\right]:=a·b^{\text{'}}·c$ for all $a,b,c\in S$. The resulting ternary algebra $(S,[\left]\right)$ satisfies the para-associativity law $\left[\right[abc\left]de\right]=\left[a\right[dcb\left]e\right]=\left[ab\right[cde\left]\right]$, which defines the variety of semiheaps. Important subvarieties include generalised heaps, which arise from inverse semigroups, and heaps, which arise from groups. We consider the intermediate variety of near heaps, defined by the additional laws $\left[aaa\right]=a$ and $\left[aab\right]=\left[baa\right]$. Every Clifford semigroup is a near heap when viewed as a semiheap, and we show that the Clifford semigroup...