It can be successfully argued that the job interview is the most important part in the search for new employees. This is when you, the nonprofit manager, will truly get to know the prospective employee. A job candidate may look flawless based on their resume, but you might find that they are not as great after an interview. While it would be ideal to conduct one interview for every individual, you will find that it is much more beneficial to interview those candidates that are most exceptional a second time.
In general, the first interview is more of a "getting to know you" affair. You should be looking to find out if the candidate is truly the person they claim to be on their resume. You will ideally have too many candidates to interview for it to be wise to try and figure out if they will be "the one." Treating the initial interview as a kind of filter, therefore, will make it easier to figure out who will be the best fit for your organization.
And that is why it is so advantageous to conduct multiple interviews. While it would be best if you could figure out exactly who you want to hire based on one interview, it makes a lot more sense to have multiple rounds. You will undoubtedly be faced with prospects who don't live up to their resumes in the first round. By weeding out these individuals, you will have a better chance of finding out who is the best person for the position when you begin your second round of interviews.