In an interesting attempt to side-step the sovereign immunity set out in FSIA, the AG of Missouri sued the Chinese Communist Party over Covid-19:
On Tuesday [Apr 20?], Missouri’s attorney general filed a suit seeking damages for harm to Missouri and its inhabitants. The suit was praised by Donald Trump Jr. as “a very appropriate move.” [...]
The Missouri AG attempts to avoid the Foreign Sovereign Immunities Act (FSIA) by arguing that the Communist Party of China (CCP) is not covered by the FSIA, and that the CCP “exercised direction and control” over all the other named defendants.
Courts generally do not view attempts to “plead around” the FSIA favorably. The complaint cites an unpublished opinion by a federal district court in Michigan finding that the CCP does not fall under the FSIA, but that determination was inconsequential, because the plaintiff’s claims had other fatal defects. However, in a different unpublished opinion, a federal district court in New York found in a decision, upheld on appeal, that China Central Television is an instrumentality of China because it is the “mouthpiece of the Chinese Communist Party.” Similarly, a federal district court in Florida found that the Communist Party of Cuba is an agency or instrumentality of Cuba, a designated state sponsor of terrorism under the FSIA. On the other hand, a New York district court issued a default judgment against ZANU-PF, whose First Secretary was Zimbabwean President Robert Mugabe (the judgment was overturned for improper service). [...]
The Missouri complaint also names the government-run Chinese Academy of Sciences, which allegedly administers the Wuhan Institute of Virology. Even if these entities end up falling outside the FSIA’s definition of a foreign State or an agency or instrumentality of a foreign State (which is unlikely), the Supreme Court indicated in Samantar v. Yousuf (2010) that the FSIA would apply when the State is the “real party in interest.” This observation provides a basis for treating the suit as if it were filed against China, if the plaintiffs seek assets from China. In addition, the Republic of Philippines v. Pimentel (2008) holds that a suit may not go forward if a sovereign foreign State is an indispensable party, which China would very likely be here. Finally, if a defendant falls outside the scope of the FSIA, that defendant must be properly served with process, and there must be a basis for asserting personal jurisdiction over that defendant (in addition to subject-matter jurisdiction over the claim).
So clearly the issue of instrumentality is probably going to be central here with respect to FSIA even if the Chinese Communist Party (or the Chinese Academy of Sciences) is named in the lawsuit. The snippets I've quoted seem to cover most such relevant precedents in which the instrumentality of the party in a single-party system was discussed in court.
I'm curious however if there are cases in US courts where a political party from a [foreign] country not featuring a single-party system was sued in US courts. And were such lawsuits successful in bypassing FSIA?