Can I do: 72 Hr Beijing on arrival, and 144 Hr Shanghai etc on departure?

Hi there!

I am a Canadian passport holder.

I am wondering if I can fly into Beijing, enjoy 72 hour free stopover and then fly to a third country within Asia and stay in that country for about 10 days.
Then, fly from that third country after my 10 day trip (probably Singapore or Thailand) to Shanghai, and enjoy the 144 hr free stopover on my way back to Canada?

I am just wondering if it is possible to do both within one trip (stopover on the way there and also on the way back)

Thank you in advance!