How much do you normally oversize the AC upstairs and the furnace downstairs on floors that have open stairwells? I currently have a 3 story house with 1 HVAC system per floor that is properly sized (runs almost 100% during the hottest and coldest days) but my stairwells now are closed off, when I open them I know that it will cause a huge stratification effect. The only other thing I can think of is a duct that goes from the first floor to third floor that circulates air up or down depending on the season.

Contractors do not oversize systems for the reasons you speak of.

A load profile is done for each floor. During this profile the designer takes into consideration what is above and below each area being conditioned.

What I understand you plan to open up the stairs for what ever reason. Your concern is that the cold air from each level will sink down to the ground level and all the heat will rise?

Typcially the location of the return ducts takes into consideration the falling or rising conditioned air. But to re-duct your home would be a lot of money and a lot of hard work to adapt the change your doing.

What type of stair area are you talking about? And how are they blocked off? There are many methods of keeping air on each floor but each method used is dependent on how the home is constructed.
Are you just using one heating system and three cooling units, or does each level have their own heat and cooling system?
Once we have this perhaps we can help with some better answers.

I had worded my question wrong. Assuming the system sizes below, after opening up the staircases how much larger would the AC be on the top floors and heater be on the bottom floors?

It is an old Victorian house with those grand open foyers, during the WW2 housing boom they built a wall down the middle of it to split it into apartments.

I have 3 heating and cooling systems, one for each floor. First and second are 80k btu (output) and 3 ton AC, third is 40k btu (output) and 2 ton AC.

Both the furnaces and AC are nearing 20 years old and all of the duct work was poorly installed almost 50 years ago so I will be replacing both the HVAC units and ducting regardless so I have a pretty open slate.