Hello Steve,
Loren, at GoldenKnots.com is an excellent resource on tying Turks Heads. I will try to explain in words, but Loren also has some great photos, and may even have a video on Turks Heads.
When you tie a 3L x 4B TH, it looks like an endless 3 strand braid going around the circumference of the band. If you give yourself a little room in the knot, it is possible to add bights to the knot without adding leads using only the working end of your line. This is what I meant when I said to extend the braid.
Generally, when I tie a 3L x 4B TH the standing end enters the knot with an 'over', so these instructions will be for that kind of knot. If the standing end enters the knot with an 'under' you will need to reverse these instructions, or turn the knot inside out.
To increase a 3L x 4B Turks Head in the normal manner, take the working end, and cross over the standing end. Then follow the standing end (over1, under1) to the top of the knot. Then cross over the standing part again, and follow it back down to the bottom of the knot, and crosso over the standing part again. Where the working end comes out of the knot is very close to where the standing end enters the knot. Now take the workng end and cross under the standing end, and you will see the two parallel lines you have just laid down, this is the standing end, and your last pass of the working end. Split those two lines, and you will have a channel where you will have to go contrary to the over unders so that the lines that cross the channel will also be over under. When yoou get to the top of the knot, and have crossed under the stading part, you will see another channel which must be split, and the tied to continue the over under pattern. You will emerge from the knot where the standing line enters the knot. You are know holding a 5L x 6B TH. Repeat as neccesary, adding crossings for the added leads, to 7L x 8B, 9L x 10B, etc.
Each time you 'extend the braid', you will need to do another cross over go up, cross over go down, and then split the extra channels. Extending the braid also changes the ratio of added leads and bights when you increase a TH.
If you are still confused, we can Skype.
Pat