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Monster Hunter Stories was on 3DS, and MHS2 is about te release for Switch. Instead of catching monsters during battle, you steal eggs and hatch them to raise your own monsters. Then battles are 2v1-3 with you and a monster against wild creatures that can battle solo, in pairs, or even 3 at a time.
You can also ride your monsters, each one has a field skill based on its family, and each area is pretty large and open with secrets to find.