Path intersection to simplify selection process

Hello,

I selected the bridge you can see in the picture below with the pen tool and now I would like to select the inner parts of this bridge (underlined in red in the screenshot), because the outer edge has already been selected, I would like to take advantage of the intersection mode ton only have to draw with the pen tool the inner edges but I don't know how to connect the new anchor points with the first global path, I tried to hover it but nothing happens it draws a new anchor point...
With a marching ants selection it works perfectly but I would like to keep the individual paths of each part of the bridge...
Thank you in advance for your help !