This is a major misconception that many people seem to have. The incremental protection offered by additional layers, beyond the first 2, is almost negligible. What you need to ensure are:
- the outer box is of high quality, i.e., it cannot be easily punctured#
- The product is tightly packed inside the box*. There shouldn't be any space for the product to move inside the box, otherwise it will constantly experience shocks from within, regardless of how well it is handled.
Apart from this, if your product is soft (e.g. LCD screen without glass cover, speakers), then you need to put a layer of soft plastic/fabric and add a hard board/thermacol before wrapping it in bubble wrap.
And finally, please ensure that the package is easy to open. I once received an NVMe SSD where the sender had tightly wrapped the SSD in cardboard with multiple layers of tape, then pasted this with very strong glue on the box itself. Trying to pry the SSD from the box made me feel like I was going to bend and damage the SSD. Then there was a time where I got a mini PC where I couldn't tell which way I was supposed to open the box from. I was trying to open one side when the PC just fell out of the other side. All your packaging is a waste if it causes the receiver to damage the product while opening.
* this is a point which many professional sellers also seem to not understand. I have received many packages from Amazon where the package had layers and layers of wrapping outside and the product was moving freely inside the oversized box. This kind of packaging is useless as the product can break from shocks inside the packaging itself, there's no benefit of the outer packaging.
# thickness is not an indicator of how easy it is to puncture paper box. While thick box is better than thin, high quality paper is harder to puncture, hence better than just thick but poor quality. Look up burst factor of packaging paper. Use box which feels hard and sturdy, it's better than using thicker box of low quality material.