I may not understand the question correctly... but in EOS language, there is only ever one Integrator per company. As Travis said, the Integrator is defined as LMAing the senior leadership team.
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Reminder: you begin with the idea that every org has three basic functions: sales/marketing, ops, finance/admin. Decide whether you have three major functions or more (up to 7). But once you decide that, you need to designate a single leader for this team: the integrator.
Textbook definition of the integrator is the person who LMA's the leadership team. By that standard, you can only have one integrator. People can only have one boss, and teams can only have one leader.
That said, the functional heads can basically be "integrators" of sorts for their departments. The head of the department may have several team leaders reporting to them and need to break ties, get people to play nice, etc. This is a very integrator-like role.