The multi-valuation ideal conjecture for unstable dp-finite fields

Let $\mathbb{K}$ be a monster model of an unstable dp-finite field. A multi-valuation ring is a finite intersection of valuation rings, and a multi-valuation ideal is an ideal of such a ring.

Multi-valuation ideal conjecture. There is a small submodel $K \preceq \mathbb{K}$ for which the infinitesimals $I_K$ contain a nonzero multi-valuation ideal.

The source proposes this as a strategy for attacking the Shelah conjecture and the classification problem for dp-finite fields. Its resolution is not given.