The function takes a string input, iterates through the string, and alternates the case of each character. Then, it appends an additional character to the end of the transformed string, which seems to be related to the sum of the indices of uppercase characters.

[CODE]: Here's a Python code approximation that represents the behavior of the function.

```python
def modified_string(input_str):
    result = []
    for i, c in enumerate(input_str):
        if i % 2 == 0:
            result.append(c.upper())
        else:
            result.append(c.lower())
    
    extra_char = chr(ord('A') + (sum([1 for c in result if c.isupper()]) % 26))
    result.append(extra_char)
    
    return ''.join(result)
```

Let's test a couple more cases to confirm the behavior.

COMMAND: PYTHON(./temp/function.py "alternation" "example" "iNpUt" "UPPER")