Just to be clear: You have a shop press, and various sized discs for different diameters; such as below: I have these sets, lots of places sell identical ones. The large set will arrive with a damaged case. I filled mine with expanding foam and it made the base of it usable for storage. The lid had basically been broken off in transit.
Small/medium -
https://www.amazon.com/dp/B06Y5KX5TM/?tag=atomicindus08-20
Large/XL+ -
https://www.amazon.com/dp/B07G549QHM/?tag=atomicindus08-20
However you have nothing to "receive" the item you are pressing out? You are also without a press ram-extension, leaving you to space your ram down with sockets, or constantly raise/lower your base plate?
For ram extensions, we have some adapters from an old brake lathe. Various sizes, works great. Something like these.
https://www.amazon.com/dp/B07MJTW1Z4/?tag=atomicindus08-20
https://www.amazon.com/dp/B00WXMUXM8/?tag=atomicindus08-20
https://www.amazon.com/dp/B015EEWUVI/?tag=atomicindus08-20
This is a great receiving cup set, awesome for control arm bushings. Various places rebrand it. It says not for use in shop presses, but I've maxed out the shop 20 ton a few times. They have a cut-out down one side, so you need to be careful not to crush them inwards pushing them through a hole that's too small. Break it free, then go down a size.
https://www.amazon.com/dp/B07WD8QMVW/?tag=atomicindus08-20
Good quality bearing splitters are a must have; mine are proto. Various companies make them, sadly the quality ones are pretty much all expensive. USA made and a known brand are what you want. Set your width, and press you victim out the bottom of the press. I have a 4x4 setup underneath the press with a piece of plywood angled on it. As anything falls through, it hits the wood and gets defected into the wall.
As you press more things, you can save things and make your own adapters. For instance, after pressing out a wheel bearing, the old bearing outer race makes a perfect adapter for pressing in the new one. All of that, a master ball joint kit and on-car wheel bearing kit, and you can pretty much press anything you can fit in the press.
EDIT: signcrafter posted a nice on-car wheel bearing tool, which has some large receiving cups. The ball-joint press style cups are usually no more than 2.5 inches around. Kythri posted the set of those I have; along with an Astro C-frame kit.