Do pokemon typically have only one egg at a time, or can they have clutches?

It depends on the species, anonymous. Some of the smaller, more mammalian pokémon only lay one egg at a time, as do humanoid pokémon. (They can lay multiple, but this is rare.) Larger pokémon as well as reptiles, birds, and insects all lay clutches, and pokémon that are more inorganic in nature lay a varying amount of eggs, depending on how much material exists around them. For example, geodude can lay more eggs if it forms its nest underground, in rocky terrain. It lays fewer eggs if above ground and indoors.

In short, I suppose you could say the answer is, “Yes, they can have clutches, but not all of them do.”