How do you fix it? There's nothing illegal about other parties- heck they are always out there. The only rules out there are participation support in election systems. But other than that...
Amend the Constitution to ensure one person / one vote and to impede the buying of offices and bribes. It's not magic - there is nothing sacred or natural about the status quo. We make big changes, same as our forefathers did when they wrote the Bill of Rights, passed the 14th Amendment, began to interpret the Constitution as a document protecting human beings over property post-Lochner. We have a reformist wave that adapts our system of government to our times.
Appearances aside, the way to fix democracy is more democracy.
If I became God Emperor for 24 hours:
0. Spending is not protected speech.
1. A state gets one Senator and then one more for every 10M people in the state. So, Wyoming has 1 Senator and California has 4. Wyoming is still wildly over-represented, but the Senate is more democratic and a handful of rural red states cannot hold the entire country hostage.
2. All political contributions must be by individuals of voting age, and must be made to a single candidate standing for a single office. Cap the maximum political contribution per person at 10% of the median personal income of individuals of voting age. Illegal contributions are confiscated, plus a fine of 1000x the overage, payable to a national non-partisan election integrity fund. All political contributions are public information -- both the contributor and the recipient are 100% transparent -- contributions must pass through a non-partisan registration house in between them. All campaign funds not spent by the candidate on that race go to the integrity fund. No PACs, no unions of concerns voters, all media on behalf of candidates is spending.
3. You cannot lose the right to vote for anything short of treason. No criminalizing blacks to rig elections.
4. Election tampering is treason.
5. End the Electoral College.
6. Eliminate all executive pardons.
7. Federal judges serve lengthy but fixed terms (say, 20 years). Nominee must be deemed fit by the ABA or a non-partisan agent. Senate may advise and have hearings but does not confirm.