How to say thanks in this situation?
Imagine you want to thank someone. For example you can say: 'Thanks a million'
Now, I'd like to thank someone more than a million. Imagine the words 'Infinity' and 'Unlimited'.
Can I say: 'Thanks unlimited'? and 'Thanks infinity'?
What can I say in this situation?

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You'd say 'I can't thank you enough'.

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No, they sound silly.

Why not use "thanks" in general, and save "thanks a million" for when you're very, very grateful? :)

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Thanks, it means a lot. - Thanks a million is kinda corny, if you're trying to be sincere say it means a lot.

If it is in person say thank you and maintain eye contact.

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You could say "Thanks a billion."

Haha, it's not commonly used but it does make sense and it's definitely more than a million :P