I knit continental style and I think
I understand what you are asking... A couple of weeks ago I was trying to work out how to do this cute "woven-look" stitch which sounds kind of like what you are describing.
In this stitch, you had to knit the second stitch on the left needle WITHOUT slipping it off, then knit the first stitch, and THEN slip both the stitches off together. This is effectively a "left twist" which causes the stitch to look "criss-crossed" (I think you can use this method to do cabling without using a cable needle in order to make the cable "twist").
The trick is that when you knit the first stitch (which is the second stitch on your left needle), you have to knit it from the back. Amy has a great video on this site on how to do this:
It's called "knitting through the back of the loop"
For cables you can knit multiple stitches together through the back of the loop.
Sorry if I am misunderstanding your question and describing something entirely different!