Yes, you can. But how?? Well let me explain this to you.
First of all, on your current account you can have 2 more different farms. These farms are a gourmet farm and a flower farm. The gourmet farm will be offered to you by an old lady in a quest at level 20. However, at level 20 you can only buy it for gold. If you have a bit more patience and wait until level 25, you can buy it for farm dollars. The flower farm will be offered to you by a young lady at level 35 for gold and at level 40 for farm dollars. These farms are similar to the main farm and can be accessed through the farm signs outside your farm, the drop down menu in the top middle of your farm and the next harvest menu on the right.
Want to start over with your current account or create another account? Even that is possible. But only on a different server! (or delete one of your accounts on your current server). One farm per server. To give a hint, most countries have an own server and an international server. Do you want to go to an English only server? Then you might want to join US1, UK1 or AU1! You can find more information about servers here: (click).