When your organization clogs up with an excessive number of concurrent projects, and juggling tasks and working on weekends don't help any more, it's NOT a sign that you need to hire more people. Probably it's sufficient to eliminate bad multitasking.
Delays in the simultaneous execution of many projects usually do NOT result from a lack of resources, but from wasting their capacity as a result of pervasive bad multitasking.
Bad Multitasking is a situation in which we juggle too many tasks at the same time. That makes all projects much longer, creates excessive fatigue and a large number of errors.
The solution to the problem of bad multitasking is to freeze a significant amount of work in progress (at least 25% but occasionally more than 80%), and gradually defrost them (in accordance with project priorities).
A practical tool for managing the queue of projects is kanban.