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We show that the $h$-vector of a $2$-dimensional PS ear-decomposablesimplicial complex is a pure $\mathcal{O}$-sequence. This provides astrengthening of Stanley's conjecture for matroid $h$-vectors in rank $3$. Ourapproach modifies the approach of combinatorial shifting for arbitrarysimplicial complexes to the setting of $2$-dimensional PS ear-decomposablecomplexes, which allows us to greedily construct a corresponding puremulticomplex.

Pure $\mathcal{O}$-sequences arising from $2$-dimensional PS ear-decomposable simplicial complexes