You can try. But each periodical has different guidelines about what reprints they accept. Many stipulate that they're only interested in previouysly unpublished work.
But in most cases the rights return to you within a certain period post-publication, so you can try flogging the piece elsewhere.
You might try to resell the work to a non-competing market - a publication whose readership does not overlap geographically with the one you've just had the piece in. If the magazine is only distributed in Ottawa, you could try a regional magazine elsewhere in the country - or overseas.
Don't overlook other English-speaking countries. New Zealand, Australia, Britain, South Africa... and many countries do publish in English, even if it's not their national language.
Anthologies often include previously published work, so watch out for those putting out calls for submissions.
Your best bet is to check each individual publication's guidelines to see if they accept previously published work. And check the contract or agreements you sign with any periodical to see how soon the rights return to you.
The best writers are also good marketers. If you can get extra mileage (and $$) by reprinting you essays, articles, short stories, and poetry, you're doing well.
Check out the following websites for useful market listings.
Worldwide Freelance Writers
Jacqui Bennet Writers Bureau (UK Listings)
Writing-World guidelines and guidelines databases
Yahoo media by region