The top row is carpenter blocks with the hex plating on it to emulate the middle row, which is the chisel block large hex plate. The bottom row is to just show how the chisel blocks change what is rendered.

There are two issues here, one with the textures lining up and parts of the blocks not being rendered. The first issue I'm guessing would be difficult to deal with for slopes etc, but the chisel block changes is texture so they "connect".

The second issue is when the chisel block is on the carpentry one and not fully being rendered. Currently, I have only seen this problem with blocks from chisel, but blocks from other mods may exhibit this also.

These are some of the blocks I quickly tested, and the lava, water, and hex have the render issue, but the futura, technical, and fan blocks not only render properly, but also render the movements on the sides (the fan spins, etc).

This is within the direwolf20 1.7.10 1.3.1 modpack, so I'm using version 3.3.6 of CarpentersBlocks.

There is no facility for connected textures to work with this mod. And anything that custom renders blocks using layers also won't work.

Only a few mods would really benefit from a layered texture API, so sadly I don't see it happening unless someone else puts in the work. I only know of one other mod that requires this.