Every call to twinx() creates a new axis, so you want to re-use the first one:
julia> axis2 = twinx();
julia> plot!(axis2, rand(10), label="v1")
julia> plot!(axis2, rand(10), label="v2")
But to me using the twinx() stuff in Plots always feels like an uphill struggle - usually once my Plots get that complicated I switch to Makie…