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Propositional Dynamic Epistemic Logic (DEL) provides an expressive framework for epistemic planning, but lacks desirable features that are standard in first-order planning languages (such as problem-independent action representations via action schemas). A recent epistemic planning formalism based on First-Order Dynamic Epistemic Logic (FODEL) combines the strengths of DEL (higher-order epistemics) with those of first-order languages (lifted representation), yielding benefits in terms of expressiveness and representational succinctness. This paper studies the plan existence problem for FODEL planning, showing that while the problem is generally undecidable, the cases of single-agent planning and multi-agent planning with non-modal preconditions are decidable.