In the current campaign I'm running, one of my PCs has made it fairly apparent that one of their goals is to economically own Magnimar. Is there anything currently set up for this (including A: a system for purchasing other companies, B: a good way to find out how much money each business would be making him, and C: possible obstacles he could encounter along the way)?
Your player wants to buy the City of Magnimar?
I have to say, this is bold and amazing! By any means, go for it!.
First, you have to decide if you will treat the city as an independant town (a kingdom) or you want to treat it as a bunch of buildings that he can buy.
The first approach will allow you to estimate the cost of non-private buildings, so the person selling the city (the mayor) will give a price for public buildings (temples, barracks, city halls, districts, garrisons, walls, etc).
To do this, we can use the kingdom building rules to estimate the cost of all buildings. Though those rules are complex enough so you can estimate the cost of the entire kingdom, it can be narrowed down to estimate the cost of a single city. Example, a barracks lot has a 6 BP cost, which can be estimated between 2,000 and 5,000 gp each (or 12,000 to 30,000 gp).
You will have to obtain or create a list of buildings in town, or at least the most important buildings that he can buy to gain more influence. The city is classified as a large city with a population of 16,428, and it has 19 districts. But there is no kingdom sheet with all the lots used, so you will have to create it by yourself. Obtain the campaign setting book for Magnimar so you can have an idea on how to build each district. Each district here can be built as a separate town, and he could buy one at a time instead of all at tonce.
While the second approach means he is buying the city from every person in the city, even the owner of those stables, which means the city will be deserted once he bought everything from their owners. Example, a single barracks (not a lot of them), is priced as 3,700 gp.
This second approach is a much slower process and both of you will take a lot of time pricing every building available. But it can be done using the downtime rules. This approach is even more time consuming because the downtime system goes down to "rooms" that you use to create your buildings, and how much each room (and the people working on them) will grant your character as profit.
This doesn't sound like a matter for downtime. It sounds like the focus of a campaign arc. I'd suggest you run it as a major plot point rather than trying to run it as a system.
First, talk with the player, figure out what his goal is, and whether or not it's even plausible. In many cases, for example, if you buy out a business the owner will go off to do something else, taking along anyone personally loyal to them in the process, leaving you the shell of a business. If you can fill that role, that can be good, but if your goal is to also own all the other businesses, that doesn't work so well. My guess is that the player's actual wants will be served by "dominant economic force in" or "ruling merchant prince of" or similar... and scoping it properly will help write the side-campaign.
Next, keep talking with the player, and figure out what the rough intended steps would be to achieve that sort of a thing. Acquire controlling interest in this or that major corporation, acquire a monopoly on this or that vital resource, get appropriate amounts of influence over the following governmental bodies and/or roles, and so forth. Make sure that these are all things that the player can do while continuing to adventure, or that the player is willing to effectively retire their character at some point during this process.
Depending on how much of an undertaking this is, pull in the other players, and make sure that they'll be okay with it. If the player can somehow manage his takeover in off time, that's great, but it seems a lot more likely to me that this will require concerted effort and adventuring parties doing adventuring party things. If so, you'll want to make sure that the other PCs are okay with "Control Magnimar" as at least a secondary focus of campaign. Make sure that you're okay with it too. If you don't get buy-in and/or you personally don't want to make it a campaign focus, then they may have to scale back and/or delay their goals until it is the sort of thing they can do in their off time.
At that point, assuming you have buy-in, just start building out adventures for it like any other adventure.