First of all, I LOVE griffin silk and nylon thread with the built-in needles. I use that thread the most often for my stringing projects. When I run out of thread on the knotting side (because you WILL run out of thread on anything longer than 24" with double strand knotting) here is what I do.
If using beads with large enough holes to accommodate the triple strand of thread, move to the next step.
1. If stringing pearls with a smaller drill hole, carefully cut the "end" knot (what will be the end of your strand holding the pearls waiting to be knotted) and pull the remainder of pearls/beads off the thread onto your stringing board. If your end piece is really short, consider working the knot out of the string so you won't run too short on this end.) Once the remaining beads are laying on your beading board in order, take the next 3-4 beads/pearls to be strung (the last 3-4 you pulled off) and enlarge the hole with a reamer or pearl bit and drill. This will need to be done to facilitate 3 threads passing through all 3-4 of your beads/pearls.
(Again, If your holes are ALREADY large enough to accommodate 3 threads, move on to the next step.)
Once you've reamed out the 3-4 pearls, thread a beading needle at the end you "cut or unknotted" and re-string the newly drilled pearls back into place all the way to the end of your project, leaving room for the knotting.
2. Taking a new piece of Griffin thread, tie a knot above and below the strand you are stringing onto using the new thread and the too short needle thread that needs to be extended. Once this knot is secure and there is a 3-4" tail on the NEW thread, thread BOTH needles through the next bead. Tie a standard "loop" knot around the 2 strands existing, thread BOTH needles through the next bead and repeat until you get to the last larger reamed pearl.
3. Now that you have 1) tied on the new string, 2) tied 2 more knots between beads with the 2 strings, you are ready to take BOTH needles through the 3rd (or 4th) bead and do that "double knot" that you started with, making sure that you leave the shorter needle piece dangling. Continue your 2 thread knotting to the end of the strand and finish as always.
4. When you are done, take some of the stringing glue and secure the double knot and "dangle string".
5. Let the glue dry and trim close to the pearl/bead.
I've successfully used this method to string with Griffin Thread on longer strands. I save the smaller left over pieces from projects to string bracelets AND to use on the longer strands that just need a bit more thread.
Hope this makes sense, and it helps you.