Hi Helminator
It's good you are thinking about setting up a new tank for your corys. You will enjoy them even more when they are in a species tank because you can keep a larger number of them and so they will be even more playful.
The exact number that you can keep depends on the level of nitrate in your tap water and the frequency of water changes you would like to do. Since the end product of the beneficial bacteria that consumes the fish waste is nitrate, and this is what you want to remove when you do water changes, if your tap water has low nitrates you will be able to keep more than if it is high to begin with.
Let me suggest that after you set up the new tank, you take some of the filter media out of your filter and add it to the new filter. You will immediately be able to add the three corys you already have. If you fill it with 1/4 to 1/3 full with the water from your present tank, it will help keep bubbles from forming on the sides and get it off to a good start.
In a week or two add a few more and let the beneficial bacteria reproduce. If you repeat this until the nitrate level starts moving up at the end of the week (or when you would normally do a water change) you can add enough corys to fill it, without adding too many.
I like to keep the nitrate levels at 30ppm or lower, but it could go to 40ppm without problems. Above that, it's more of a risk, and I start doing more frequent water changes. See how this works?
If you are starting out with low nitrate tap water, and do you water changes weekly, I would say that you could easily keep 10 albino C. aeneus, perhaps even more.