[aephi alum]

It's up to you how you want to structure things. As a local, you have lots of flexibility.

One of the points of a pledge / new member program is to give your new members a "trial" period during which they can learn about the sorority and get to know the sisters and their pledge sisters well enough to decide if they want to go through with initiation. A risk of having a NM join an existing class halfway through the NM period, is that that NM's education will be rushed and she will not have as much time to experience that "trial" period, bond with her pledge sisters, and make a fully informed decision.

On the other hand, if a NM joins a week or two into the pledge period and is dedicated enough to "catch up" to the existing NM class in her education, it might be best for her to join the existing class rather than become a pledge class of one. It's less stressful on your new member educator and on the sorority as a whole (i.e. having to hold two separate initiations).

My chapter has done both. We've integrated a new NM into an existing class that was one week into their NM period, and we've had overlapping NM periods and two initiations in the same semester. In both cases, it worked well.