A fully modular system inside a 3x3 or 4x4 (with 1 block/1 lamp per level) is impossible because of the lack of space to fit repeaters or redstone torches in a configuration that will still respond correctly to an on/off switch.
The tallest tower that I could make respond correctly to an on/off switch was this 3x3
Which uses an upside-down half slab in the middle and next to the unlit lamps and is powered by a redstone torch underneath a solid block (instead of a half-slab) in the middle of the bottom level
The smallest size of free standing tower that I could fit a fully modular system in was a 3x3 with 2 blocks and 1 lamp per level, controlled from the bottom
This is the first part of the control system (there's a redstone torch on the inside side of the block with the torch under it)
This is the second part of the control system (there's a solid block in the middle of the cross)
If you built the tower against a wall however, it is possible to fit a fully modular system inside an apparent 3x3 like this