Realistically, no. Because it’s not a game of chance. Theoretically anyone could. Practically you live in a system where voting for small parties is punished by the lower of two evils losing votes and the greater of two evils not.
Following scenario: let’s imagine the Mildly Evil™ Party and the Very Evil™ Party had a votes split of 55:45. Mildly Evil™ would win. Now we introduce party C, that is neither. The party can either appeal primarily to Mildly Evil™ voters or Very Evil™ voters. Very Evil™ voters are currently, overall, not unhappy with their party/candidate, since they like how evil their party is, while Mildly Evil™ voters don’t like that their party is as evil as it currently is, so it’s safe to assume, it’s gonna be the Not Evil™ Party. Now, Very Evil™ voters are not significantly going to vote for the Not Evil™ Party. Maybe a little less than a tenth of them will. And maybe a little less than half of Mildly Evil™ voters might vote something else, thus the Not Evil™ Party. The result would be Not Evil™ with 30%, Mildly Evil™ with 30% and Very Evil™ with 40%. Very Evil™ wins, the rest lose. Only the one with the most votes can have power. Your votes for Not Evil™ made Very Evil™ gain that power. And that’s including the unrealistic notion, that you could get half of all Mildly Evil™ voters to vote for a new and unproven party at all.
Now, let’s take a better scenario based on different set of rules (aka the rules most other democratic countries live by, where parties need an absolute majority to govern): let’s take those three parties again and the same results, Not Evil™ with 30%, Mildly Evil™ with 30% and Very Evil™ with 40%. Now, Very Evil™ have the most votes but they don’t have the absolute majority, so they cannot rule alone. They’d have to find a partner. However both Mildly Evil™ and Not Evil™ would never work with them, because they are too evil for either. However, Mildly Evil™ is just about not evil enough, that Not Evil™ would consider working with them. Together they have 60% of votes and thus the absolute majority, forming the Almost Not Evil™ coalition for that term, building a foundation for Not Evil™ to grow until the next election.
This is the only way how voting for a small party can realistically work. Of course, usually there are more than three parties. Here in Germany, for example, there are more than a dozen, most of them too small to matter, thus there being a 5% hurdle for small parties, so the government is not so split it couldn’t function (that’s part of what killed the Weimar Republic and helped the Nazi Party to gain power in the 1930s). There are usually between 5-7 parties large enough enter the government and there are usually two to three parties in a governing coalition. It’s not a perfect solution but it gives smaller parties a fighting chance. In a system like the US, where a party just about needs to have a simple majority to win, not an absolute majority, smaller, independent parties almost never even have a chance.
And unless you change the system that supports that you’ll be trapped with the same two flavors of madmen. And you obviously cannot change the system in the right direction if you cast your vote to either someone who would love to be dictator or to someone who is too small to even have a voice.
Since the civil war, there hasn’t been one president who wasn’t dem or rep. The only one coming somewhat close was Teddy Roosevelt who, in 1912, split the Republican Party into two, after not being nominated, founded the Progressive Party and subsequently lost the election for himself and the Republican Party. [Results: Woodrow Wilson (dem) 41%, Roosevelt (pro) 27%, William Howard Taft (rep) 23%]. Were the Republican party not split, they might have won. And Roosevelt was an established politician and ex president at the time. Like, you’d need someone like Obama to found a new party, be allowed to run for another term and not only beat the Democrats but also the Republicans in the actual election. That’s just not realistic, even if it were actually possible.