No, you can't. The only way you can truly prevent states from having their interests overriden by a majority of the nation is to give them a direct role in the legislative process.
Democracy is three wolves and two sheep voting on what to have for dinner. It's last thing we want. So when the three wolves invite the two sheep to join them in a democracy, the sheep wisely say "Not a democracy, but a federal union, with an upper house in which votes are allocated by species rather than population, then we will join your nation". Now the wolves may moan that this is anti-democratic, but they agreed to it, as that's the price paid for getting the sheep to join with the wolves. The sheep are the small states, and the wolves are the large states.
So anti-democratic structures are good. But at the same time, giving the population input is also good. We want popular pressures to have a veto, but not to be able to force legislation onto states without their consent.
Similarly, we want the states to have a veto but not to force their legislation onto the nation as a whole without the public's consent.
This is the balance -- a mechanism to limit mob rule while also requiring mob consent. Seriously this is not some strange thing I should have to explain -- these issues were all debated during the discussions surrounding the adoption of the constitution, as you can read in the Federalist Papers. See especially no. 10.
https://founders.archives.gov/documents/Madison/01-10-02-017...
It is why we do not live in a democracy, but in a Federal Republic. The house is the hotbed of populism, that's where all the crazy stuff happens, and the senate is the moderating force that can filter it out. The house then has to moderate its positions and pass something that the states also consent to.
And that's exactly how it's played out. The senate always moderates or blocks extremist measures coming out of the house. The founders were amazingly prescient.
Moreover this obviously leads to better and more stable government. Control of the house flips from red to blue to red every 5-8 years. Now imagine a nation's entire base of laws constantly flipping back and forth that often.
As an example, when the GOP controlled the house in 2017 they tried to pass a tax bill to completely eliminate the SALT deduction. The Senate moderated that to 10K max. Now the democrats control the house and they want to make it (effectively) unlimited again. The Senate will block that. In 2024, say when the GOP is back in control of the house, they will try to eliminate it again. The Senate will block that. The 2017 house eliminated Obama's ACA -- but the Senate blocked that. Just think of all the whipsaws in policy we would have if healthcare is massively reconfigured every 4 years. So you need to do more than just get 51% to redo healthcare in America. That's how it should be. Yes, it's anti-democratic, but thinking you can rewrite a nation's laws with 51% is foolishness. It's a recipe for secession and civil war.
In other words, going from 49% to 51% doesn't mean you go from 0 to 100% power, but rather you have to settle for 48% of what you want, and then 51% of what you want. The removal of that discontinuity creates stability in government.
It is intentionally, and wisely, anti-democratic, while also being intentionally, and wisely, anti-aristocratic. Both sides need to come to a compromise, and this stability is why our constitution has lasted as long as it has.