Sure! Here's a Python function that generates test cases for the given problem statement about calculating the maximum possible Manhattan distance between two points on a 2D plane.

```python
import random

def tcgen():
    # Number of points on the 2D plane
    N = random.randint(2, 2 * 10**5)
    
    # Generate the list of points
    points = [(random.randint(1, 10**9), random.randint(1, 10**9)) for _ in range(N)]
    
    return N, points

# Example usage
if __name__ == "__main__":
    N, points = tcgen()
    
    print(N)
    for x, y in points:
        print(x, y)
```

### Explanation:

1. **N**: This is generated randomly within the given constraints, i.e., between 2 and 200,000.
2. **Points**: Each point (x_i, y_i) is generated such that both x_i and y_i are random integers between 1 and \(10^9\).

### Example Output:

Upon running the `tcgen` function, you may get an output like:
```
4
123456789 987654321
135792468 246813579
102938475 564738291
192837465 564738291
```

This provides a valid input for the problem statement.

Feel free to adjust the random seed (using `random.seed()`) if you need reproducible test cases.