Yes. Weakening any one of the conditions of the conjecture gives different opportunities for generalization, and any one condition can be relaxed in different ways. This is also true of mathematical objects, not just theorems. Consider something simple like a vector space: We can think of this as a field acting on an abelian group by scalar multiplication, and one immediate generalization is to ask "why only a field, why not a ring?", which leads to the theory of modules. We can also take a vector space and look at the relationships between subspaces: We can decompose a vector space into subspaces, and each of those subspaces has a basis. A subset of those basis vectors defines another subspace contained in the first. The relationships between these subspaces can be represented as a combinatorial object, and rather than studying vector spaces *per se*, we can study these combinatorial objects that satisfy the same basic properties as the subspaces of a vector space. This leads to the theory of *matroids*.