You are a team member
The target system is usually defined for the entire team of a large project, not individually in each small team that is part of a larger project. This is done precisely to allow systems thinking to coordinate activities, rather than simply giving some people a thinking advantage over others. It is not about a competitive or sports-like thinking of competition and victory, but about thinking in terms of agreements and collaboration.
As a team member/internal project role, it is not necessary for you to be involved in working on the target system in its entirety. You could be working on developing a subsystem for the target system, or even a subsystem of a subsystem - but it would simply be your personal opinion that you are working on "your own target system." You could keep this opinion to yourself. You are dealing with your system (of course, everything in the world is a system!), but not the target one. Within the project, in communication with the team, you should still talk about the sub-system entrusted to you or even a subsystem of a subsystem (you can even call it "my system", it won't confuse anyone), instead of demanding that the team acknowledge your system as a full-fledged target system for the entire team.
You may also be involved in developing an enabling system (for example, implementing a project to develop a department within an organization), where you will not be directly working on the target system. But this does not mean that you should consider the department as the target system for the entire project. In the overall project, you need to create hairstyles, and within your project - create the department. These are two separate projects, and you should not consider them as one. You should not think that the target system for you is the one that will be the enabling system for everyone else. No, your target system is the same as everyone else's, which changes through the work of enabling systems, including those enabling systems that you create in turn - meaning your systems. If you organize an aviation plant, then the target system is the airplane. If you consult the organizers of the aviation plant, you better consider the airplane as the target system, not the organizers!
Just like in maps, each person does not build a map with polar coordinates around themselves. People have agreed on the North Pole as the origin of coordinates on a global scale - and everyone on Earth uses the same reference system, the pole doesn't move according to the whims of a single person or even a single team of travelers, it is common for everyone. The systemic approach recommends such an approach: to agree on a common target system for the entire large project team.
The project team is not necessarily a project group under your leadership! Most likely, in this "we," you occupy a couple of role positions, doing a part of a larger task, not holding the entire system in mind, but dealing with either a separate practice/culture/trade (e.g. heating engineering, management, programming, choreography) or part of a system. If you have a part of the whole system, it will be "our system" for the small team or "my system" for you personally.
Regarding this, it is quite possible and necessary to develop a full systemic thinking. The first step here is to find the target system to determine the place of "our system" relative to it. It is important to carefully identify that target system with which everyone will agree, synchronize actions in relation to which everyone will act, and then deal with the system that is closest to you.