This isn’t realistic.
What do you mean by “a good chunk?”
The last 3rd Party candidate that earned even a respectable number of votes was Ross Perot in 1992. He won 18.91 % of the Popular vote, but failed to win any states in the Electoral vote.
I would call 18.91% “a good chunk”, but it didn’ get him anywhere near the Presidency as, like Secy of State Hillary Clinton, he failed to take into consideration the Electoral College, which, thank God, prevents the Presidency from becoming a "popularity contest."
There was a lot of talk at the time that Mr. Perot cost Pres. Bush (old Bush) the Presidency, as Gov. Bill Clinton won and became our President, and we ended up with 8 years of fun and food and sex scandals (remember the cigar?) and an impeachment and all the rest, and of course, First Lady Hillary Clinton making a mess out of her attempt to create a national healthcare system. But at least Pres. Clinton was great for business–the economy did well during his Presidency, and he was very likeable (according to a poll of Secret Service, he was their favorite President to work for).
A “good chunk” of popular vote will not make the system finally fall apart. From what we have seen in American history, what will make the system finally fall apart is when a majority of people recognize that a political party has a platform that is objectionable, based on false premises, racist, and out-of-date, and simply stop voting for candidates in that party. However, when this happens, a new political party rises to fill the gap and create a new 2-party system.
I do agree with you that it is unfortunate that we don’t have several viable politicial parties. I wish we had a system like Germany where several political parties (4?) earn seats in their governing body.
However, I don’t think this is likely because we have such a melting pot of races, nationalities, ethnicities, religions, income levels, etc., and 50 states that are extremely different in their climates, topographies, tourist appeal, business development, etc. We would end up with dozens and dozens of political parties and it would be difficult for any one party to muster up enough votes to win the Electoral College and hence the Presidency.
But it would sure be nice to see a plurality of parties in the House and Senate instead of the two warring parties constantly locking horns and getting nothing done.