Hey Ahmad,

I don't know if I understood you correctly. I think you are looking for a protocol to overlap three PCR Product, am I correct?

Assuming that's what you are looking for, I will mention how I do such Overlapping PCR. I usually do it in 2 step. First is 4X cycle followed by 25X cycle.

In 4X Cycle, I add 2X premix, all 3 PCR templates (higher concentration ~10ng/ul the better in our experience) and water. Please note, there is no Primers for extension of the product at this step. The annealing temperature for this 4X PCR reaction use the annealing temperature for overlapping sequence of 3 PCR templates.

Then, take out tube and add both primers and carry our 25X PCR reaction with annealing temperature of the two Primers used.

I hope it helped. Good luck and please let me know if you have any questions.

Please check overlap extension PCR cloning by AV Bryksin. Best wishes

I've been told to try using the templates themselves as primer for the 10 first rounds of amplification and then adding the primers and doing the remaining cycles. Give us information about the length of your sequences.

https://www.researchgate.net/post/PCR_overlap_extension_with_a_small_29bp_overlapping_region_Tm67C_Should_I_worry_a_72C_extension_step

They are 464 bp, 765, and 1173 bp.