Question

Why we can't find a relation between a physical quantity depending on more than 3 quantities using dimensional method ?

Answer 1

Formally saying : Buckingham pi theory

Informally : you have three arbitrary scales to set in most problems (mass, length, and time). [Occasionally there may be other scales, like temperature, but these are usually set by other constants, like Boltzmann’s constant.]

This means that you can eliminate (at most) three quantities by setting them equal to 1 by varying your units. If you have one left over (call it
x), then the formula could be anything in terms of that remaining quantity - any f(x). So you can’t do anything with that.