Hi, thanks for your query. Yes there is a filter available that will give you those results.
Start by visiting the All Sydney Private Schools page. You can get there from the Find Schools menu on the right side of any page. Once you're there click the grey button near the top of the list - "Filter these results". That allows you to pick criteria such as school type, gender, international students accepted etc. Select "International Students (CRICOS registered school)" and any other criteria you require and click the "Find Schools" button. You'll get a list of schools that match. Easy!
Here is the list already filtered for you...