Does anyone else want licensing for a third computer?

What the others said. Your use case sounds very typical of many Cloud users.

You can sign in (activate) and sign out (deactivate) of devices at any time. I call this toggling. I, too, toggle my activations between several devices, particularly when travelling. 

If you don't need to be signed in to three devices at the same time and are happy toggling two activations then you'll be fine with one Adobe ID.

If you already have two devices activated and try to activate on a third device with the same Adobe ID, then the apps on your third device will prompt you to deactivate (sign out) on other devices.

You can also sign in to https://account.adobe.com/activated-devices and see which devices are already activated (maximum of two at one time). You can remotely deactivate a device from that page too.

For travel, install on 3rd device and deactivate your other ones.  I have CC installed on 4 devices but only two are activated concurrently.  I can use only one device at a time anyway.  I'm not an octopus.

Team plans are available for multi-user enviroments.  But by the sound of it, you don't need a Teams plan for personal use.

I agree, depending on your usage, it can be awkward or intolerable. The only way to get more than 2 licenses TO BE SIGNED ON AT THE SAME TIME is to set up more Adobe IDs and take a subscription on each one. I did that. But if a quick signout/signin isn't a problem you don't need to do that. Your use case (travel computer) seems like that should be OK.

sure you can.

you can install the cc desktop app from here https://creative.adobe.com/products/creative-cloud on as many computers as you own and use it to install all (or some, if you want) of your cc subscription programs. the only (insignificant for internet connected computers) limitation is that you can sign-in (and therefore start your adobe programs) on, at most, two computers at any one time.  

because you can sign out from either (or both) signed-in computers using a 3rd computer, this could not (imo) be easier.

https://helpx.adobe.com/download-install/using/install-apps-number-of-computers.htm