A company grows people wise because they have a lot of things to do and try to achieve all of them. But is it a good idea for an organization to linearly grow a number of projects with a number of people? I don't think so.
Be aware of the pitfall
Before you have the new people on board, you are most likely end up with your existing people dealing with to many projects at the same time. You get used to this unhealthy pace where everybody is some kind of overworked. This is unhealthy for the people (burnout) and unhealthy for the organization because people try to finish things earlier without thinking about negative consequences that may appear.
This can easily become your default behavior - == even for the new people! ==
Doing the better way
Instead of blunder into a trap of doing more and more projects with more and more people you should start to prioritize!
If you don't have time, you don't have priorities.
This is all about being efficient and being effective. Many smart people how are working in a company setup like this will be very efficient and complete one task after another. But they are not able to step back and see the bigger picture. They won't see it after finishing one task after another. They are trapped and so they are not able to think about what would be the right thing to do. Or just: how to be effective.
What to do in such an environment?
Imagine you are new to such a company, all people around you just dealing with their projects. Many of them at the same time. Beside that you will find many open projects were nobody is pushing forward. It's also very likely that somebody will ask you to take over some projects - for sure there are many. This is the moment where you need to step back, meditate about the work and the working streams going on around you. See the bigger picture and don't go into the trap of try to do all of the open things. You will never accomplish this task, there are too many things to do. As soon as you are able to resist the stress around you, you can prioritize what's the best thing to do instead of doing all. Then do this one thing right! And afterward start a new prioritization.