Does adding solutes to water alter its triple point?
Triple points are typically defined as points on the phase diagram of a pure substance where three phases coexist. Their existence requires that the phase rule be observed, which is $$f=C+2-P$$ where $$\begin{align}f &amp;: \text{number of degrees of freedom} \\ C &amp;: \text{number of components} \\ P &amp;: \text{number of phases}\end{align}$$ The number of degrees of freedom is the number of intensive variables that can be altered independently while remaining in a given phase. 

In general, when three phases coexist, $$f=C-1$$ If the system consists of a pure substance, $f=0$, as expected (the coexistence region corresponds to a point). If you have a mixture of $C$ components (labeled $i$), you will observe a different triple point for each choice of $C-1$ independent mole fractions $\chi_i$. But for each combination of mole fractions, coexistence of three phases will still occur at regions corresponding to single points.