The U.S. recently briefly had a three party system with the emergence of the Tea Party. All it did was radicalize the GOP. Just ask John Boehner.
Arguably this radicalization was only possibly because of the Hastert Rule. Under the Hastert Rule the smart strategy was to only caucus with the GOP, and obstruct the GOP when they didn't get what they wanted. That provided the Tea Party with maximum effectiveness. Without the Hastert Rule and some other technical developments, the Tea Party could have and would have occasionally shifted their support.
Another way to look at it is that without the Hastert Rule and similar mechanisms that bolster the power of parties, a two party system is largely a two party system in name only. What matters isn't the number of nominal parties, but the effective autonomy of individual representatives. You don't need 3 or 5 or 12 parties, which in almost every country invariably come to represent niche interests (similar to all the caucuses in Congress) but otherwise usually align with one of the main parties. You can have the same outcomes so long as politicians and informal caucuses can more easily defect. Not only will they defect, but it softens the official stance of the remaining parties.
We don't need to copy the structure of multi-party European systems. Rather, if we want the same outcomes[1], we should understand the dynamics and replicate or the types of dynamics that matter. Without the latter, simply copying the structure is unlikely to be effective. With the latter, copying is unnecessary.
[1] That assumes the outcomes are different and desirable. But the notion that multi-party systems tend to more centrist and inclusive politics seems stale to me. The rise of populism and even nationalism has hardly been confined to traditionally two-party systems, like in the Anglosphere. Heck, when it come to issues of abortion and immigration the U.S. has always been and remains more liberal than almost every European country.