Double-increase variations

There’s a double increase that’s commonly created by “knit-one-yarnover-knit-one-in the same stitch.”
If you diagram it without indicating the way the threads cross, it looks like this.

Without showing how the threads cross, it’s not clear what structure is being created. So, I thought, what are the possible ways to pull three loops through another loop? I have found three essentially different ways (that don't involve twisting the original loop). Two of them have a reverse side that looks different.
1. First is the knit-one-yarnover-knit-one that’s familiar:

You can create this same structure by performing a purl-one-yarnover-purl-one on a reverse-side row.
2. Another is knit-one-yarnover-purl-one. This is a completely reversible structure. It looks the same and is created the same way on both sides of the fabric:

If you do purl-one-yarnover-knit-one, you get the mirror image of the diagram above.
3. A new (?) one is what I tentatively call a knit-squared. You pull a loop through a loop towards you as in knitting, and while keeping the “legs” of the new loop as separate loops, pull the head of the new loop through the old loop towards you again. I am not sure how to efficiently produce it in hand knitting, but the structure is like this:

These are the three different structures (I don’t count the reverse sides of this as different) I’ve found to “disambiguate” the first diagram.