Fixpoint iteration constitutes the algorithmic core of static analyzers. Parallelizing the fixpoint engine can significantly reduce analysis times. Previous approaches typically fix the granularity of tasks upfront, e.g., at the level of program threads or procedures - yielding an engine permanently stuck in one gear. Instead, we propose to parallelize a generic fixpoint engine in a way that is parametric in the task granularity - meaning that our engine can be run in different gears. We build on the top-down solver TD, extended with support for mixed-flow sensitivity, and realize two competing philosophies for parallelization, both building on a task pool that schedules tasks to a fixed number of workers. The nature of tasks differs between the philosophies. In the immediate approach, all tasks access a single thread-safe hash table maintaining solver state, while in the independent approach, each task has its own state and exchanges data with other tasks via a publish/subscribe data structure. We have equipped the fixpoint engine of the static analysis framework Goblint with implementations following both philosophies and report on our results for large real-world programs.