Here's an example:
"The cat, that was black and fluffy, chased the mouse, that was grey and timid, through the garden, that was overgrown with weeds, until it reached the shed, that was made of wood and had a rusty door, where the mouse, that was now trembling in fear, squeezed through a crack, that was barely big enough for it, and escaped."
This sentence uses "that" seven times, and it is grammatically correct because each "that" is used as a relative pronoun to introduce a dependent clause, specifying the cat, mouse, garden, shed, crack, and mouse's fear.
Let me know if you have any other tricky grammatical questions!