EF1+PO for agents together with EF1 for market values

Determine whether, for every instance of fair division with additive subjective utilities u_i and a single additive market valuation v, there exists an allocation that is simultaneously envy-free up to one good (EF1) and Pareto optimal (PO) with respect to the subjective utilities (u_i), and envy-free up to one good (EF1) with respect to the market valuation v; equivalently, establish whether a balanced EF1 allocation satisfying PO w.r.t. the subjective utilities can be guaranteed when the market valuation demands equal division by value.

Background

Every allocation is trivially PO w.r.t. market values, so the interesting trade-off is achieving PO w.r.t. subjective utilities alongside fairness under the market valuation. The paper shows that PO cannot be achieved together with SD-EF1 on the market side, but does achieve PO (indeed fPO) w.r.t. subjective utilities together with EF1 w.r.t. market values when subjective utilities are strictly positive.

The open question asks whether the stronger combination EF1+PO w.r.t. agents and EF1 w.r.t. market values (or even just balancedness, which coincides with EF1 when market values are identical) exists in general.