I would say you’re referring more to complexity than determinism. More variables increases complexity but doesn’t necessarily decrease determinism. It depends on whether you believe some of those variables include true randomness though. For example, does quantum randomness affect anything? We’re led to believe it has no real effect on a macroscopic scale, but perhaps over a large enough amount of time and across a large enough set of variables the effect becomes noticeable. If that’s the case, determinism breaks down.