Membership Upgrade Path

I have two levels of paid membership on my site. "Level 1" is, let's say, $1 and "Level 2" is $2. These Memberships are indefinite, with no time limit.

I want "Level 1" members to be able to upgrade to a "Level 2" membership for $1 (they already paid $1 for "Level 1" so they just need to pay an extra $1 for "Level 2"), but I also want regular visitors to have the option to purchase "Level 2" at the regular $2.

So my first thought was to set up another level called "Level 2 Upgrade", make it $1, and have it be only available to "Level 1" members, but I'm not sure how to do this, since anyone will have access to purchase that level if they know the direct URL.

Is there anyway to restrict the signup page for "Level 2 Upgrade" so only "Level 1" members can access it? Or, is there another way to set this up?

Thanks in advance for any help.