northwind“You can't eat your cake and have it.
You can't eat your cake and have it
too.
You can't eat your cake and have it
either.
I think the first and the sencond sentences are correct and the first sentence could have the same meaning as the second.
I can't judge the third sentence. It's so tough.”
You're okay. "Too" means "also" here. You're right that the first two sentences mean the same thing.
The two things we're talking about here are the verbs. There are two verbs describing two actions.
It would be equally grammatical to say "You can have your cake and eat it too," but you might be telling a lie.
"You can't drink beer and drink wine at the same time. It will make you sick." This statement may or may not be true.
"I can drink beer and (drink) wine at the same time. It doesn't make me sick." This may be a lie.
So,
"I can / can't drink beer and (drink) wine too / also." These statements are all argumentative. Can you or can't you??
"I can have my cake and eat it too, because after I eat it I still have it in my belly."
The "too / also" is not necessary. It's just for emphasis. "I can do them both." "I can't do them both."
I can have a wife and a girlfriend too.
I can't have a wife and a girlfriend too.
Worry about "either" tomorrow. It doesn't fit in these sentences. It only works when both options are negative. "I can't have a wife or a girlfriend either." "I can't eat my cake or have it either!" (Poor guy!) 
"I can't have my cake and eat it either" is ungrammatical." (You must use "or.")
I can have both A and B.
I can't have both A and B. (Some people have trouble with this one. The "can't" applies to the word "both,"
not to "both A and B." It does not mean you are forbidden from having A
and forbidden from having B. You're allowed to have one or the other, but not both.)
I can't have either A or B.
I can't have A, or B either. (These last two mean the same thing.)
I can have A and I can have B too.
I can have A but I can't have B too.
I can keep my car or I can sell my car.
But I can't keep my car and sell it too.
My car has been reposessed. I can't keep my car or sell it either!