"Make something up" is a command given to someone when you want them to make an excuse so others won't be asking any more questions.

"He can't make something like that up!" is said when you know someone is speaking the truth because the information or reasons given given by this person are too complex or indepth to be dismissed as a lie; therefore, it is assumed to be true.

"You can't just make that up!" would mean that the person you are speaking to should not be foolish enough to think he or she can lie about (a specific) something and then expect to get away with it; it won't be credible. Or perhaps it would be credible, but it would be considered unfair. Whether or not it is credible would depend on the situation.
For example: Ed manipulates Sally into skipping one of her classes. Sally worries and tells Ed that her teacher will ask where he was during class. Ed responds by saying: "Make something up", meaning she should just lie to her teacher by saying she had something important to do (when really she didn't).

Second example: A six year old tells her mother that she saw her father kissing with a red haired woman in the car when she took a peak through her bedroom window. When her mother confronts her husband and he denies this, the girls mother could say: "Well, she can't make something like that up!", meaning the daughters information is so specific and also considering her age, it can hardly be dismissed as a lie.

Third example: A boss want to fire his secretary for not doing her job right. The secretary says that if he does so, she will tell the entire office that they slept together. Her boss could say: "You can't make that up", meaning it is unfair to him because it never happened.
by rick1990 July 3, 2014
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