How do I fix my fireball spawning twice when 2 people have the ability to do it?

I have an npc that gives you the ability to press e and you throw out a fireball. When one player in the server alone has the ability to do so it spawns one fireball but when two players have the ability when e is pressed two fireballs spawn, and so on with more people.

This script is the keypress and cooldown and stuff.

local RS = game:GetService("ReplicatedStorage")
local remote = RS:WaitForChild("Fireballe")
local plr = game.Players.LocalPlayer
local mouse = game.Players.LocalPlayer:GetMouse()
local animation = plr.Character:WaitForChild("Humanoid"):LoadAnimation(remote:WaitForChild("Hit"))
local cooldown = false

mouse.KeyDown:Connect(function(key)
    if cooldown == true then return end
    if key == "e" then
        cooldown = true
        animation:Play()
        wait(.2)
        remote:FireServer()
        wait(3)
        cooldown = false
    end
end)

This script is the fireball.

local RS = game:GetService("ReplicatedStorage")
local remote = RS:WaitForChild("Fireballe")


local tweenservice = game:GetService("TweenService") 
remote.OnServerEvent:Connect(function(plr)
    local fireball = game.ReplicatedStorage.Fireball.Part:Clone() 

    fireball.Parent = workspace 

    game.Debris:AddItem(fireball,3)

    fireball.CFrame = plr.Character.HumanoidRootPart.CFrame + plr.Character.HumanoidRootPart.CFrame.lookVector * 15

    tweenservice:Create(fireball,TweenInfo.new(3,0,0),{CFrame = plr.Character.HumanoidRootPart.CFrame + plr.Character.HumanoidRootPart.CFrame.lookVector * 70,Transparency = 1},Enum.EasingStyle.Quint,Enum.EasingDirection.Out):Play()

    local alreadytouched = false 

    fireball.Touched:Connect(function(hit) 
        if alreadytouched == true then return end 
        if hit.Parent.Name == plr.Name then return end 
        if hit.Parent:FindFirstChild("Humanoid") then 
            hit.Parent.Humanoid.Health = hit.Parent.Humanoid.Health - 20
            for i = 1,#hit.Parent:GetChildren() do 
                if hit.Parent:GetChildren()[i]:IsA("Part") or hit.Parent:GetChildren()[i]:IsA("MeshPart") then 
                    local fireparticle = game.ReplicatedStorage.Fireball.Fire:Clone()
                    fireparticle.Parent = hit.Parent:GetChildren()[i] 
                    game.Debris:AddItem(fireparticle,6) 
                    alreadytouched = true 
                end
            end
            for i = 1,6 do
                hit.Parent.Humanoid.Health = hit.Parent.Humanoid.Health - 3
                wait(1) 
            end
        end
    end)
    wait(2.3)
    alreadytouched = true 
end)