Add to subplots within a loop using Plots.jl?

I am trying to plot some data I have and am having trouble with using subplots. The way things are structured, I need to be able to add data to each subplot incrementally within a loop, then combine into a final plot afterwards. Here is my MNE (minimum non-working example):

x = 0:0.1:1
p1 = plot()
p2 = plot()
p3 = plot()
for i = 1:3
    p1 = scatter!(x, x.+i, leg=false)
    p2 = scatter!(x, x.*i, leg=false)
    p3 = scatter!(x, x.^(i), leg=false)
plot(p1, p2, p3, layout=(3, 1))

Doing it this way, all the data seems to get pushed into p1 leaving p2 and p3 blank. Is there a way to get this to work?

edit: The goal is to have something that looks similar to this:

for i = 1:3
    scatter!(p1, x, x.+i, leg=false)
    scatter!(p2,x, x.*i, leg=false)
    scatter!(p3, x, x.^(i), leg=false)

Well, that was easy. Thanks!