How would a company increase projected operating income without increasing the total sales revenue?

Operating income is basically profit before tax and interest. The only way it can be increased whilst sales revenue remains static is to reduce cost of sales and/or all other expenses as operating income = sales - cost of sales - overheads/expenses.

There's various things to consider like getting the same supplies from a different supplier offering a cheaper price or negotiating a better discount from current suppliers which would reduce the cost of sales.

A big one is employee productivity: can the same volume (or more) of work be done by having fewer staff employed to do it, and, can those staff be managed by fewer managers? Big savings could be made there on salaries.

Expense accounts can be looked at individually to see where cost savings can be made - is all post going out first class mail, is the stationery supplier value for money or charging over the odds?

Basically everything that is a cost to the business would need to be looked at to see where savings could be made on those costs without impacting on the sales revenue.

Having said all that, "Without impacting on the sales revenue" is important, because any business can reduce its costs by getting rid of staff or getting cheaper supplies or whatever, and that might work as a quick fix, but the long-term result is likely to be that the cheaper you try to do something, the costlier it will be in the long-run. So the key is Value for Money to sustain revenue levels, rather than what is the cheapest way of reducing costs.