Once a substitution is made on a parent molecule, its structural symmetry is usually reduced, meaning that atoms that were formerly equivalent may no longer be so.  Thus substitution of two or more equivalent atoms by the same element may generate more than one positional isomer.
The classical example is the derivatives of benzene.  Its six hydrogens are all structurally equivalent, and so are the six carbons; because the structure is not changed if the atoms are permuted in ways that correspond to flipping the molecule over or rotating it by multiples of 60 degrees. Therefore, replacing any hydrogen by chlorine yields only one chlorobenzene. However, with that replacement, the atom permutations that moved that hydrogen are no longer valid. Only one permutation remains, that corresponds to flipping the molecule over while keeping the chlorine fixed.  The five remaining hydrogens then fall into three different equivalence classes: the one opposite to the chlorine is a class by itself (called the para position), the two closest to the chlorine form another class (ortho), and the remaining two are the third class (meta).  Thus a second substitution of hydrogen by chlorine can yield three positional isomers:  1,2- or ortho-, 1,3- or meta-, and 1,4- or para-dichlorobenzene.
For the same reason, there is only one phenol (hydroxybenzene), but three benzenediols; and one toluene (methylbenzene), but three toluols, and three xylenes.
On the other hand, the second replacement (by the same substituent) may preserve or even increase the symmetry of the molecule, and thus may preserve or reduce the number of equivalence classes for the next replacement.  Thus, the four remaining hydrogens in meta-dichlorobenzene still fall into three classes, while those of ortho- fall into two, and those of para- are all equivalent again.  Still, some of these 3 + 2 + 1 = 6 substitutions end up yielding the same structure, so there are only three structurally distinct trichlorobenzenes: 1,2,3-,  1,2,4-, and 1,3,5-.
If the substituents at each step are different, there will usually be more structural isomers.  Xylenol, which is benzene with one hydroxyl substituent and two methyl substituents, has a total of 6 isomers: