redle's response sums it up. I'll just add that each new brothel costs more and requires you control more businesses. (eg, to get the 2nd Brothel, you need 10,000 and 30 businesses, the 3rd required 30,000 and 50 businesses).
You'll get a naming box each time you say 'yes' to the prompt if you'd like to buy (you only get a confirmation prompt if you meet the requirements, otherwise it will tell you you need X amount of gold and X amount of businesses) MAKE sure you name it something different than your other brothels (obviously) but ALSO make sure you don't have the same name as you do in other save games, as it apparently crashes the game if you do. (IE make each name of every brothel in every game is unique to avoid random but persistent crashing) I don't think you can re-name any brothels except your first one. (rename the save/.gam files to do that)
You'll buy each new brothel sequentially and have up to six (or five?) you can own. After the last one, there are no more icons, therefore no new brothels to purchase. But you can always 'Add Rooms' in every brothel. You can have up to 255 rooms in each brothel, so a maximum of 1275 girls (if the limit is 5 brothels, or 1530 girls if it's 6 brothels). I don't think we have 1500 unique girls (yet!) so there isn't really a cap!
You'll find 'Add Rooms' under the Brothel Management screen (where you set allowed sex acts). If you don't see it, you don't have any of the 1.30 versions, as 1.29 and under do not have that option. There is no boxes informing you that it has expanded (but you will get a 'not enough gold' if you don't have 5000g for each click, or a Max rooms reached box if you have hit the 255 rooms limit) You will have to go back to the main management screen, and look at the 'rooms available' stat up in the top right hand area to see your new max. capacity. If you didn't get any boxes when you clicked 'Add Rooms', it should have gone up in multiples of 5 everytime you clicked it.
