Can you put a speech mark after a speech mark?

For example, "Hi David" said Max, "Hi Max" Said David

Yes.

Here is the correct way to punctuate that sentence.

"Hi David," said Max. "Hi Max," said David.

Ohh now I can continue my story thank you Ms.Sue

You're welcome, Lilly.

Yes, you can put a speech mark after a speech mark, but in most cases, it would not be necessary or grammatically correct.

In the example you provided, it seems like you are trying to show a conversation between Max and David. Here's how you can properly format the conversation using speech marks:

"Hi David," said Max.
"Hi Max," said David.

In this formatting, each character's dialogue is enclosed within a pair of speech marks, and a comma is used to separate the dialogue from the speaker's name or attribution. Including an additional speech mark after the first one in each statement is not needed and may disrupt the proper structure of the quotation.