This is a vague question asking about the existence of a mathematical object, instead of properties of a well defined one. I am sorry if this is not the correct forum.
I know if you have a random graph $g \in G(n, p)$ on $n$ vertices ($n$ large) where each edge is included with probability $p$, as you increase $p$ from zero there is a very acute point where the probability that $g$ is connected becomes almost certain. That it goes from the state of "being disconnected" to "being connected"
I am wondering if there is discrete structure $s \in S(n, p, q)$ on an underlying set of size $n$, parameterized with two probabilities $p$ and $q$, over which you can describe three mutually exclusive states. In such a structure can there exist a point $(p_t, q_t) \in [0,1]\times[0,1]$ that in a reasonably small neighborhood (with an $\epsilon$ which shrinks as $n$ grows) each of the states become almost certain. A mathematical equivalent to a triple point.