I don't know if your three-layer cake is a small 6" or a full sheet cake, but I'd suggest using skewers/dowels (not for support, but to help prevent the layers from sliding) even if you aren't transporting it anywhere. It could potentially slip moving it from your turntable to your kitchen table!
When making taller tiers, I'll insert a cake board 1/2 way up (3-2" layers split becomes 6-1" layers...board after 3-1" layers then the remaining 3-1" layers) mostly for ease of serving...taller tiers would require larger dessert plates...they would hang off, or darn close, the edge of the average dessert plate.
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