You would do a flat tax on anything above X, where X is essentially a number calculated on base living costs in your area for the number of people in your household. Anything above X is taxed at a flat rate. This ensures people can afford to live and meet their minimum requirements. It also makes it so that the tax code is extremely simple.
For me personally - I would add one more change that most people don't like. I would put an actual cap on total income tax that can be paid in a single year. The reason for this is that these progressive systems act as a social welfare system that transfer money. That's why people propose a flat tax. Well, flat tax is much better but still presents the possibility for a wealthy person to pay, for example, 200k in income tax in a year. A lot of people would say "so what?". Well, I believe income tax shouldn't be treated as a maximum pain threshold. The basis of taxation is to fund public goods. We all consume roughly the same amount of public services on average. If someone is paying something like 200k a year in income tax they are paying way, way above anything they could possibly consume in public goods/services for that year.