Linear algebra problem

The fish to be commercialized, has to meet four linear requirements on: weight, length, circumference. 
If p, l e c are weight, length and circumference, a linear condition is written as ap+Bl+yc-d=0 (a,B,y,d \in R).

We acknowledge that there's no fish that can satisfy all four conditions, so we decide to edit them, adding with arithmetic to each of them a term like a,t for each i=1,...,4 where a_i are real numbers and t is the time passed since the fish has been fished. A kind of fish is the quadruplet (p,l,c,t). With this condition we are sure that at least one kind of fish exist that meets all 4 new requirements. Is it possible that there are infinite kinds of fishes that meet all the edited conditions?

a) no, just 1 kind max

b) yes, no matter how are the original conditions chosen

c) if and only if 3 max of the 4 conditions are linearly independent

d) Only if the new 4 conditions are linearly independent