There are some pets that have a high chance of spawning together with two to three others of the same or very similar type. They can usually be found wandering around in a pack. When you engage in battle with them, you'll almost always find the second and third pet are the same pet and quality for each one.
Because they're essentially cloned teams, this can be somewhat frustrating when hunting for a certain one. The only way to generate new teams is to force a new spawn by removing the pets through defeating them in battle or killing them.
But engaging in a Pet Battle with each one can be time consuming, and killing all of them doesn't guarantee a new spawn in the immediate area. Sometimes pets share the same spawn as other companions, so in killing one, you're taking a chance that the right one you're looking for will spawn in its place. It might not happen in the end.
Instead of killing or defeating all of them, I've found a better way that utilizes these groups of pets. It doesn't always work, but it's pretty effective when it does.
Instead of removing all of the companions in the group, I opt for removing most of them and leaving one behind. If there's one that stands out, I normally don't kill or battle that one. For example, in the image above, I would leave the large Tolai Hare alive, while defeating the other four.
I've found that by leaving one behind, others will quickly respawn to join it, but with a differnt second and third pet on their team. By being able to identify the original pet of the group, I can avoid battling that one since I already know what the team make up for that companion will be. Instead, I can focus on the freshly generated pets that have new teams.
If they repsawn quickly enough, I can just sit in one area for a while and hunt for a rare version of that pet within the respawning group. It removes the time required to find the pet, and any travel time to get from one to the next.
Like I mentioned earlier though, this doesn't always work, and sometimes even if I leave one up, others won't respawn. Other times it might take some time for them to respawn, in which case it's more efficient to find another group or another pet to battle.
But so far, this has worked about 90% of the time for me. It can take a while for a rare to actually pop up, though. Yet when compared to having to search for single spawned pets and trying to find a rare amongst them, the time used is comparable imo.
I hope this information helps others in their search for rares. Good luck and happy hunting. :)