Can I apply an unused non-refundable ticket towards a new refundable ticket?

It depends on the airline and the exact fare rules as to whether you can apply an unused non-refundable ticket towards a new refundable ticket. In many cases yes, though it is important to consider that this will make the new ticket non-refundable even though it would have been refundable if purchased outright. If you are purposely selecting a refundable ticket you probably won’t want to do this.