Custom zoom steps. Render new tiles at 4x. ie., Split each tile to 16 tiles in new layer.

[bibinjacobpulickal]

I have tiled images at zoom levels 2.5x, 10x and 40x corresponding levels have 4, 64 and 256 number of tiles. Is there a way I can render these tiled images flawlessly?
I tried quite a number of methods. Here, each tile is split into 4 tiles in the next zoom level. But, my requirement is to get 16 tiles for each tile in previous level.