Sanguine and melancholic sit in opposite corners of the field: one is high activation with high stability, the other is low activation with low stability. To be strongly both, a person would have to be on both sides of both axes at once. The arithmetic says the same thing: sanguine outranks choleric exactly when stability is above the middle, and melancholic outranks phlegmatic exactly when it is below. Those conditions cannot hold together, so if sanguine leads your formula, melancholic is never second.
What remains is four pure types, eight adjacent pairs in a fixed order, and one balanced profile for people close to the centre. Thirteen identities, all reachable, none invented to make the list longer. A profile counts as pure when the leading temperament is at least 14 points ahead of the second, and as balanced when the distance from the centre is smaller than 7 points.
The thirteen profiles->