Try not to think of light as an aura that is visible. Think of light more like moving particles. While not a perfect analogy, par is more like water exiting a hose measured in volume over a period of time. Don’t think of it like volume in a stationary tank.
Two lights that provide 100 par max at a given distance together will provide 100 par each, that 100 par will be illuminating their area the lenses or reflectors have directed the light. If their beams intersect, you will have some additive effect.
You can have a light that can provide up to 1000 par over a 18”x18” area, and place a clam 3” outside that zone, and while it will be receiving some light, it will not be receiving the full 1000.
Another bad analogy but may help understand some more. Just think of it like brightness. The reason that is a bad judgement is because your eyes are very sensitive to yellow and green. So you can have a violet and red light that is putting out scores more par than a yellow light, but the yellow light may appear brighter. But….two lights of equal color compared, the brighter one will be providing higher par. Two dim lights next to each other don’t make the area illuminat brighter, the dim light just covers more area.
It is far more scientific than that, but I’m trying to put it in understandable language that is digestible if the higher order concepts are proving troublesome. And that’s ok if they are
In short. To get more par, you need either more watts (will give more par overall), higher efficiency(more par overall), or tighter focusing by reflectors or lenses (more par over a smaller area). Adding more lights can work too but that is from light overlap and it won’t be a direct linear relationship of adding them together