Bit serial cpu's can they do 18 bits?

I have this great design for 18 bit cpu, that I plan to emulate.
The concept here is one extra address bits,is used for
byte addressing, and the other address bit for longer opcodes
and floating point.

Later I want to build it, but all alu’s are 4 bits wide.
Can a 18 bit serial cpu work for me? I need 8 registers, Mar
and Mdr, but no MQ. 18 bit addressing,9 bit bytes.

I see no constraint on a bit-serial ALU or CPU as to width.

But on the other hand, it seems no great hardship, if you want an 18 bit design and only have 4 bit building blocks, to build with 20 bit internals but connected and used in such a way that the overall result is 18 bits. Or if you prefer, build 16 bits with MSI components and construct the other two bits with LSI. (Or build everything with LSI!)

Since this is 18 bit octal machine, I plan to use PAL’s and have 3 bit alu.
3 256 x 1 ram 74S201 is used for the intial design 2.5 uS , but 256x4 ram CY7C122
(15 ns) ram is planned for higher speeds.