How to damage multiple people?

You can use a table (dictionary) and index the table with the player's name or user id:

local remote = game.ReplicatedStorage.BarrierBeam
local Debounce = {} -- table

remote.OnServerEvent:Connect(function(plr,mouseaim)
	if not Debounce[plr.UserId] then 
		Debounce[plr.UserId] = false -- initialize
	end
	local parts = game.ServerStorage.Classes.BarrierMaster
	local BeamLoc = parts.BarrierBeam
	local Beam = BeamLoc:Clone()
	Beam.Parent = workspace
	Beam.CFrame = CFrame.new(mouseaim)
	local dmg = game.Workspace.BarrierBeam.Damagepart
	game.Debris:AddItem(Beam, 1.7)
	wait(1.5)
	dmg.Transparency = 0.6
	dmg.Touched:Connect(function(hit)
		if hit.Parent:FindFirstChild("Humanoid") and hit.Parent.Name ~= plr.Name then
			if Debounce[plr.UserId] == false then
				Debounce[plr.UserId] = true
				hit.Parent.Humanoid:TakeDamage(35)          
				wait(2)
				Debounce[plr.UserId] = false  
			end
		end
	end)
end)