Multiple sensor circuits connecting to one counter and a 555 timer IC
The behavior you described isn't what we'd call a counter, but a kind of decoder. 

A counter increments its output each time an event occurs at its inputs, spread out over time. (Typically the "event" is a rising edge of the clock when an enable input is asserted)

It sounds like what you want is to have several inputs and to know how many of them are asserted at the same time. You can build this from a tree of adder circuits.

It's not clear why or how a 555 timer would be useful to implement this.