```python
def cap_after(passage: str) -> str:
    """
    Capitalize the first letter of every sentence in the passage,
    starting a new sentence at the start of the passage and after any full stop.
    Letters anywhere else are left exactly as they are.
    """
    if not passage:
        return passage
    
    # Split the passage into sentences using regex to handle punctuation
    import re
    sentences = re.split(r'(?<=[.!?])\s*', passage)
    
    # Capitalize the first letter of each sentence
    capitalized_sentences = [sentence.capitalize() for sentence in sentences]
    
    # Join the sentences back together
    result = ' '.join(capitalized_sentences)
    
    return result
```