As others have pointed out, the fare can increase. As soon as you add a free stopover in AMS/CDG, the luxury IX tax (and other taxes) apply and the fare increases. If you route via USA, taxes trickle up too.

Here is a ITA powertools direct booking link to delta.com for a 8 segment trip in December with stopovers on both outbound and return (at time of posting, Z class is available and this link prices out at C$ 3468.06. It will change as inventory disappears):
ITA Generated link to Delta.com for real trip


And the resulting delta.com itinerary (note, the taxes on the stopovers have increased the total fare a bit:


NOTE: All AF/KL Z fares book into J class on AF/KL flight numbers for inner-europe legs so if calculating for MQM/MQD, you get the J earn, not Z. DL flight numbers on inner-europe always book into Z which is a pain.