This is a question that has been asked many times here at AAP (and at Wifcon.com). It is not impossible to do this, but the authority depends on many factors such as:

1) Are the services under the task order severable or non-severable

2) What appropriations are being used to fund the CLIN, are they annual appropriations, what would be used to fund the extension (assuming this is not a no cost extension), are their bona-fide need issues.

3) What is the reason for the extension, etc.

If the services are severable and the rationale for the extension is not based on delays or failure to perform all of the task that the Task Order required; you are much better off issuing a new task order.