```python
def cap_after(passage: str) -> str:
    """
    Returns a passage with the first letter of every sentence in capitals, a sentence beginning at the start of the passage and again after any full stop.

    Parameters:
        passage (str): The input passage to be processed.

    Returns:
        str: The processed passage.
    """
    if not passage:
        return passage

    sentences = passage.split('.')
    result = sentences[0].capitalize() + '. '

    for sentence in sentences[1:]:
        if sentence:
            result += sentence.capitalize() + '. '
    
    return result
```