Normally, Xamarin Studio does not allow multiple solutions being open. You can, however, open multiple instances of Xamarin Studio.
You can type in your terminal the following command:
open -n /Applications/"Xamarin Studio.app"
This works fine if you need this once, but if you find that you will be doing this on a regular basis, follow the steps below:
Step 1. Open AppleScript Editor and type in the following command
do shell script "open -n /Applications/'Xamarin Studio.app'"
Step 2. Run it to check if it works. Save it with the Application format in a convenient place, like your desktop.
Step 3. You will notice that the app icon is not what you want and needs to be replaced. Go to Applications > Xamarin Studio. Right click it and select Show Package Contents. Inside the Resources folder, you will find the .icns file you need.
Step 4. Right click it the application you created earlier and select Show Package Contents. Inside the Resources folder, delete the old .icns file and replace it with the one you copied. Make sure you change the file name so it matches the one you just deleted.