Property taxes. Income taxes. Taxing people by the amount of savings they have. Importantly, don’t give the rich guys tax breaks. Give the tax breaks to the poor.
And more dollars competing for the same goods would just drive inflation higher (the rich do not directly compete with the poor in buying things, other than potentially crowding them out of real estate investments - that is a legitimate societal problem. But so is NIMBY-ism - driven largely by the fact that racial covenants and crime-targeting became illegal in the 1960s-1990s). Although we haven't really come up with great alternatives (other than drive prices up because income tends to correlate inversely with propensity for crime).
Singapore-like enforcing of laws and harsh sentences could do it (the other low-crime countries are much more ethnically homogenous), but the trade-off there is much less freedom than in the U.S. - so it probably wouldn't be palatable here.
It is also a useful tool for steering the economy.
> Taxing people by the amount of savings they have.
That's essentially what inflation does.
That is different than an explicit tax (the tax can be structured in a way to shrink everyone's purchasing power proportionally, and is harder to avoid).
It's just that the most salient example of recent deflations (2008 and 1930) happened to coincide with massive crashes and problems; but that is a feedback of deflation + excessive leverage leading into the deflation - it's not something inherent in deflation itself.