Is it possible and allowable for an organization to operate both a 403(B) plan and a SEP?

It is indeed quite possible, and a popular option among smaller non-church, non governmental tax-exempts who wish to provide an employer contribution for their employees, yet wish to avoid ERISA coverage. The SEP is provided for the employer contribution, which a Non-ERISA 403(B) is provided for voluntary contributions. Care must be taken with the 403(B) arrangement, however, to not exceed the limited involvment that the employer is permitted to have is such an arrangement without subjecting the arrangement to ERISA (DOL Regulations Section 2510.3-2(f)).

Of course, there are other plan design options that require less administration than a standard qualifed or ERISA 403(B) plan, especially for employers with no more than 100 employees (Simple IRAs and Simple 401(k) plans).