Why doesn't Team Rocket like the other supervillain corporations?

No they each have different (and conflicting) goals.

Team Rocket (Gen1/2) wants to rule the world using Pokémon, they are mainly in it for financial gain/power.

In Gen 3 two more teams come to show, Team Magma and Team Aqua who are in it for ideological purposes. Magma wants to expand the landmasses to increase the habitat of humans and land Pokémon, while Aqua wants to expand the oceans to increase the habitat of water Pokémon. And although they are in direct opposition to each other, they are also in conflict with Team Rocket. This is because if Aqua or Magma succeed in their plans, it would (negatively) affect Team Rocket, since such calamities would probably damage their income and stability.

In Gen4 Team Galactic wants to create an entirely new universe, and although it would not directly negatively impact Team Rocket, it would shift the balance of power towards Galactic... and if your goal is to pretty much rule the world, you don't want any competition.

Gen5 Team Plasma wants to separate Pokémon from humans. Seeing as all their power and revenue comes from Pokémon, this is directly against the goals of Team Rocket.

Gen6 Team Flare has similar goals as Team Rocket, this could allow them to team up but here is the problem. Both want power/wealth and both are probably too greedy to share, bringing them into conflict with each other.

Gen7 is Team Skull, they have similar goals as Rocket but are much weaker, if anything Team Rocket might assimilate them into their own team instead of working together as equals.

Also in gen7 you got Rainbow Rocket, where Giovanni recruited teams from different realities (who achieved their goal in their own universe) to work together. But this is mainly because they already won, and if it were realistic they would probably backstab each other as soon as they could claiming the other realities for themselves as well.

And Gen 8 has Team Yell, which are just some Pokémon (soccer) hooligans that take things too far. Not really an "evil" team that would ally themselves with an organization that wants to rule the world.

TL;DR
Team Rocket wants power/money/world domination... so it would be illogical to share this with another team, especially if that teams end game would negatively impact their own goals.