Typically, if my client can hold a plank for one minute in good form, it is time to add challenge. Because the plank is a static move, the body will adapt quickly and once you reach a certain point it may not be as effective. I’d rather progress my client with some movement to add challenge, rather than lengthen the time they can hold the plank.
One way to challenge the core and upper body is to either move the feet closer together (which lessens the base of support and makes the core work harder), or add dynamic movement. There are numerous ways to do this–add a pushup, alternate extending one arm, alternate a small leg lift,”saw” back and forth, and so on.
You may get different answers here, but that is how I progress. Hope this helps.