```python
def cap_after(passage: str) -> str:
    """
    Passage with first letter of every sentence in capitals, a sentence beginning at the start of the passage and again after any full stop.
    
    Args:
    - passage (str): The input string to process.
    
    Returns:
    - str: The processed passage.
    """
    # Split the passage into sentences using punctuation
    sentences = passage.split('. ')
    
    # Capitalize the first letter of each sentence and add a sentence beginning at the start
    result = sentences[0].capitalize() + '. '
    for sentence in sentences[1:]:
        result += sentence.capitalize() + '. '
    
    return result.strip()
```