Install multiple Dual edge tpu on a motherboard

Short answer - yes you can as long as You have enough supported slots, power and good cooling system but it's not that easy!

Right now it's hard to find any cheap device that support dual lane pci-e m.2 E-slot, most are 1x and only one edge tpu core will work. According to docs each TPU can take up to 3A of power and heat up above 100C. So for each core You need to think about power, cooling and supported slot which adds much more to price of whole solution. Dual TPU is now priced at $39.

For more computing power there is Asus AI board which is PCI-e 16x card with same Edge TPU cores - 8x or 16x. You will get 32 TOPS or 64 TOPS of power. Card includes cooling and PCI-e slot is usually ready for high power consumption (as for GPUs). Of course You pay about 3x for each core but that does not include price for problematic m.2 slot and cooling. I think it's still the best option.

You can consider other device with better NPU, like something from nvidia jetson family, which are ready to use devices at few levels of price and power (up to 32TOPS). Also You can cluster such devices with kubernetes and add as much as You need.

There is a PCIe adapter developed that can be used with one dual edge TPU. With this setup you could stick as many dual TPU cards onto your motherboard as you have PCIe slots. I would subscribe to the GitHub issue to get informed about additional options. Last time I talked with the creator of the adapter he mentioned to work on an adapter for a Raspberry PI but also has plans to build an additional adapter that can take more then one edge TPU.

Edit: There is a waiting list that has an option for an adapter card with 4 TPU slots.