With SHA2, there is a limit on the message size.
Is there a similar limit with SHA3?
You are right about SHA-2 having a limit:
2 ^ 64 - 1 bits for SHA-224 and SHA-256
2 ^ 128 - 1 bits for SHA-384 and SHA-512
SHA-3 on the other hand doesn't have one. Thanks to the sponge construction, you can pass an inifinite amount of bits to SHA-3 and it won't be an issue.