Multi-algebras as tolerance quotients of algebras

If $A$ is an algebra and \bgt is a tolerance on $A$, then $A\mathrm{/}\text{bgt}$ is a multi-algebra in a natural way. We give an example to show that not every multi-algebra arises in this manner. We slightly generalize the construction of $A\mathrm{/}\text{bgt}$ and prove that every multi-algebra arises from this modified construction.