Can my employer average out a large bonus over several pay periods to reduce withholding?

Yes, generally. Employers can use CRA's payroll withholding methods for irregular or lump-sum payments to average or spread the withholding calculation for a large bonus across multiple pay periods, rather than applying a single, larger withholding calculation to the whole amount in one lump-sum paycheque. Doing this can meaningfully reduce the amount actually withheld from your pay at the time the bonus is issued compared to a straight lump-sum withholding calculation.

It's important to understand what this actually changes, though: it affects the timing and amount of withholding, not the total tax you'll ultimately owe for the year. Your final tax liability is still calculated based on your complete income for the year, including the full bonus amount, at your real marginal tax rates — spreading the withholding just changes how much comes off at each pay period along the way, smoothing out what would otherwise be a much larger single withholding hit.

This is a legitimate and commonly used payroll technique, not a way to reduce your actual tax bill, so it's worth understanding the difference between "less withheld now" and "less tax owed overall" when your employer explains how they're handling a large bonus payment, since the two are not the same thing.