LeBlanc said allowing voters to cast their ballot at any polling station in their riding would require Elections Canada to adopt new technology so that a person would be removed from the voter list across the district once their ballot is cast.

Alternatively, they could trust but punish:

Don't worry about the very small fraction of people who abuse this to cast multiple ballots. Without a fairly large scale, organized effort, it's extremely unlikely for multiple votes to change an outcome under any electoral system.

Use the records collected at polling stations to identify cheaters then to throw every one of the offenders and organizers in prison and permanently prohibit any future participation in the process at all: no voting, no running, no party membership, no volunteering, no working on campaigns either directly or indirectly. Nothing, not even working as the night cleaner for an advertising agency that has political clients or a media outlet that covers or reports politics and elections in any way.

In the unlikely case that the multiple ballots are in a high enough volume to require rerunning the election, charge it to the offenders. They won't be able to pay, of course, but they'll be on the edge of poverty for the rest of their lives.