Increasing Stockinette Stitches
With the stockinette (flat knit) stitch, it helps to have some slack in the travelling yarn between the two pegs where the stitch increase will happen. I prepare to add a stitch in the row before the row where the stitch gets added. I do this by knitting a peg, wrapping the working yarn around the peg, then knitting the next peg. The first peg now has two loops on it. I remove the top loop, twist the yarn, and put the loop on the second peg. On the next row, I knit the first peg, then knit the top loop on the second peg (the new stitch), transfer that loop to the first peg, then knit the second loop on the next peg.
I did this on seven pegs on the blue loom, evenly spaced around. I then had the 31 loops needed to transfer from the 24 peg blue loom to the red loom. I knit a few rows on the red loom so you can easily see where the additional stitches were added (white lines). This technique does not leave a hole in the knit work like other increase methods do; the key is to put a twist in the travelling yarn being used to create the new stitch.
Here's how it looks off the loom (the tube got rotated).