We paid $2354 to private health plan. 3% of income is $1087. Can I submit the remaining $500 worth not covered by health plan as a medical expense?

Yes that is correct ! You can claim medical expenses for which you were not reimbursed by an insurance plan (or by way of any other tax-free reimbursement) on your taxes. If these medical expenses were paid by you (or your spouse/common law partner) for either of you or for your children you should be able to claim them.

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