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Are you coming out with us tonight?

I reply with:

I'm not sure if I can come out tonight. I want to come out but I've got a lot on my plate.

Sentence in bold correct?

Thanks for sharing and caring!
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The sentences are correct, but there's a slight problem in common usage.

This expression with "can come" usually refers to "permission." It usually applies to children.

My friends are out there; I'm in here. They want me to come out and play.

"I'm not sure if I can go out" has a little different flavor. You have your own reasons for staying in.

The expression "I've got a lot on my plate" is somewhat sophisticated, and would probably not be said by a child.
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In addition to Avangi's comments on it, your original dialog is unnaturally repetitive.

Are you coming out with us tonight?
I'm not sure if I can. I want to, but I've got a lot on my plate.