Going one step further doesn't (generally) add restrictions; it just changes them. Consider:

1. I will cooperate if I know anything.
2. I will cooperate if I know that you will cooperate.
3. I will cooperate if I know that you will cooperate iff I cooperate.
4. I will cooperate if I know that you will cooperate iff I cooperate iff you cooperate.
5. I will cooperate if I know that you will cooperate iff I cooperate iff you cooperate iff I cooperate.
6. …

Using classical logic after the modal operator, these reduce to:

1. I will cooperate if I know anything.
2. I will cooperate if I know that you will cooperate.
3. I will cooperate if I know that we will perform the same action.
4. I will cooperate if I know that I will cooperate.
5. I will cooperate if I know anything.
6. … (repeats)

Actually, now that I write it out like this, I can see why one would choose (3)!

It's important that there's an ‘if I know that’ instead of an ‘iff’, which I've seen before. But the version above is how I parsed WrongBot's statement, so hopefully WrongBot quoted it correctly. (The search function is not helping me find an original.)