Question:
Can a person ever reach a point where they can’t grow any more–a “spiritual peak”?

Answer:
You can never reach a point where you can’t grow anymore but you might reach a level of “fullness” or “completeness.”

We may become mature, but we will never know Him fully. He desired: “That I may know Him, and the power of His resurrection, and the fellowship of His sufferings, being made conformable unto his death” (Philippians 3:10). Paul forgot what he had attained to before and pressed on (Philippians 3:12-14). First Peter 2:2 says that each time you read the Word–no matter how long you have been saved–that you can learn something more. Just like: “newborn babes, desire the sincere milk of the word, that ye may grow thereby.”