If someone says: "Why don't you have a plan for a situation like this?" You can say... "I DO have a plan!"

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I'm not knowledgeable on grammar but, "I do have a plan" would be said if who you were talking to didn't believe you had a real plan. Adding the "do" adds emphasis, but more importantly it serves to convince others who might be skeptical.

The one with "do" has more emphasis that you have a plan. "Do" gives more sureness, impact and emphasis to the sentence.

Emphasis.