The supplemental jurisdiction statute, 28 U.S.C. § 1367, codifies United Mine Workers of America v. Gibbs, 383 US 715 (1966). Section 1367(a) grants jurisdiction to the federal district courts
for “all other claims that are so related to claims” over which the federal district court has original jurisdiction “that they form part of the same case or controversy under Article III.” In Gibbs, the Supreme Court held that a pendent claim is part of an Article III controversy when the pendent claim arises out of “a common nucleus of operative fact” as the jurisdictional conferring claim.
Example: If you are beaten by a police officer, then you have a 1983 claim for violation of your civil right to remain free from unreasonable searches and seizures, and you have a state tort claim for civil battery, subject to supplemental jurisdiction -- because both claims arose from the same beating.
As far as interfering with full compensation, it's not the claim that causes interference -- it's the jurisdiction over the defendant. A federal court cannot award damages against a state actor, because that would violate the U.S. Constitution
11th Amendment. Consequently, there are certain state actors (e.g., California county sheriffs) who may or may not be susceptible to legal action on a 1983 claim in federal court. Whereas a municipal policy
officer is susceptible.
However, a state actor can be sanctioned to prevent future bad actions by a federal court, so it is still possible to obtain some monetary relief in federal court.
These issues are quite complicated, and require a detailed analysis of the causes of action and the defendant's legal status, before determining in which court to sue and on what legal theories.
Hope this helps.