If the existing system does fifteen things, write down the major tasks of that system and divide them into as many verticals as necessary to describe the broad functional areas that require attention. If the replacement is intended to be a custom-developed, on-premises system, it’s perfectly reasonable for that system to be expected to accomplish most of the fifteen things in question.
However, if SaaS-based solutions are being considered as replacements, keep in mind that SaaS-based solutions are narrow and deep: they are usually highly specialized to take on a very specific vertical and are designed to integrate tightly with other highly-specialized software, feeding cross-referenced information between each other. SaaS solutions are designed to satisfy all your needs in a specific vertical, and that vertical cannot be “the entire operation of the company.”