It's hard to make assumptions on what the OP said.
It would be a violation of Nintendo's intellectual property rights
Consider the term "Doom clone" has often been used, but this doesn't necessarily mean (and usually doesn't) a clone that is an exact copy, using trademark names, or otherwise infringing on IP. "Clone" in gaming is often used in a broader meaning that meaning a literal copy - often being a shorthand way of referring to a genre, which I would hope in general aren't the property of private companies. The OP would need to elaborate on what he is after. (Admittedly, "remake" often does have stronger implications of being a direct copy, but it's better to clarify, especially as the OP talked about original storylines.)