How can I listen for when multiple bricks touch something?

First of all, since you are dealing with local parts, this has to be done inside of a local script to work.

What you are literally asking for is how to connect multiple events to the same function, which as is simple as it sounds:

local deb = false

function HitDetected(partHit)
    if not deb then deb = true else return end
    print("Object hit from " .. partHit:GetFullName())
    wait(5)
    deb = false
end

for _, v in ipairs(Parts) do
    if v.Name == "HitSensors" then
        v.Touched:connect(HitDetected)
    end
end

Place this script within a model containing all the parts you want to connect to. With this script, you're able to get BOTH the part that was touched, and the part that touched it.

function partTouched(touchee, toucher)
    --touchee is the part that was touched
    --toucher is the part that touched the touchee

end

local parts = script.Parent:GetChildren()
for i = 1, #parts do
    if parts[i]:IsA("BasePart") then
        parts[i].Touched:connect(function(toucher)
            partTouched(parts[i],toucher)
        end)
    end
end