I prove incompleteness of intuitionistic logic over monotonic and non-monotonic proof-theoretic validity (mPtV and nPtV), two kinds of proof-theoretic semantics due to Dag Prawitz. Although intuitionistic logic is already known to be incomplete over both these frameworks (Piccolomini d'Aragona 2026, Piccolomini d'Aragona & Prawitz 2026), I will provide proofs that refine the existing ones in two ways. First, the proof for mPtV has a requirement of consistency on atomic bases - while the proof of (Piccolomini d'Aragona 2026) works only if atomic bases are allowed to be inconsistent (while containing all the atomic instances of ex falso). This is important since, as highlighted by (Barroso-Nascimento, Pereira & Pimentel 2025), the requirement of consistency on atomic bases seems to play a relevant role in monotonic approaches to PTS. Second, the proof for nPtV uses a less than classical (but still non-constructive) meta-logic - while the proof of (Piccolomini d'Aragona & Prawitz 2026) uses excluded middle in the meta-language. This is important since, although a classical proof of incompleteness is enough for ruling out the existence of a constructive proof of completeness, finding a constructive proof of incompleteness would be valuable, so a proof whose meta-logic is less than classical might be looked at as an improvement towards this goal.