defining a new base of measure

In BOM I need to express - in different finished goods -  the same material with differnts unit of measure.
For example:
Finisched good: C1
Material: F1
Alternative unit of measure of F1: M1

Finisched good: C2
Material: F1
Alternative unit of measure of F1: M2

Finisched good: C3
Material: F1
Alternative unit of measure of F1: M3

I tried to define a new base of measure, but my problem is that in my case the dimension is pieces, and not lenght, not mass, not time and so on...
How can I do? How can definite a new base of measure with this dimension?