> Are there laws or money that block such thing to happen?
There are no laws backing it, and in fact the Green Party and many other parties do exist in the US. Some make it to Congress. The Presidential ballot is usually filled with a variety of different parties. State legislatures and even the federal legislature often have a little more variety. The smaller parties choose to caucus with the larger ones in what Europeans would call a coalition.
There are two political reasons it doesn't happen. Most people focus on the winner-take-all aspect of (some) final elections. This is a little misleading since not all elections are one round of winner-take-all in the first place), and almost all elections have at least a primary beforehand, making it minimally something at least akin to two-round voting.
The other reason is there's no need to. There is extremely little intra-party policing. I (I have actually done this, though I lost) can right now, make this my platform and file my paperwork to run as a Republican or a Democrat. I get the immediate benefit of all the massive party machinery in the general election if I win the primary election. When I win my election, I can push my issues to my hearts content, and by working with my nominal party, I am likely to get at least some minor legislative or executive wins. The more successful I am the more I will shift the politics of the entire party, especially if my platform proves popular with voters - more politicians in my "party" will take up my cause to help their own.
How do I choose which party? Well, I choose the party I think is more likely to work with me. I can, at any time, even after assuming office, switch parties and choose to caucus with someone else if I think I will be more successful that way. This happens more often thank you'd think.
https://en.wikipedia.org/wiki/Party_switching_in_the_United_...
The US doesn't have a ton of parties at the federal level because the two "parties" are really already representative of two broad coalitions in practice. You only see a third party rise en-masse during times of huge, sudden political re-alignments where the old coalition falls apart and a new one has to be formed. Even during "normal" times, though, you certainly have a lot of politicking based on the "real" parties within the coalition, and groups within the Republican or Democratic parties in Congress go vote with another group that aligns more with their interests. For example, the Republican party is a mix of libertarians, neoconservatives, Chamber of Commerce Republicans, Trump Republicans, and others. The Democratic party is a mix of environmentalists, social justice advocates, Chamber of Commerce Democrats, warhawks, Blue Dogs, the CBC, pro-labor folks, neoliberals, etc. It's a very messy picture and votes don't necessarily fall along coalition lines. Often, for example, the Blue Dog Democrats vote with Republicans, and Trump Republicans and pro-labor Democrats have some commonalities where they vote together. There's no rule requiring members to vote with their party, so they do as they like. If you flout the majority of the party often enough you might lose your shot at a a sweet committee assignment, but if you don't flout your party you might very well lose your election. Generally, the party will recognize when you can't vote with them due to your constituency and be perfectly ok with it.