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It was recently found that excited states of semi-vortex and mixed-modesolitons are unstable in spin-orbit-coupled Bose-Einstein condensates (BECs)with contact interactions. We demonstrate a possibility to stabilize suchexcited states in a setting based on repulsive dipole-dipole interactionsinduced by a polarizing field, oriented perpendicular to the plane in which thedipolar BEC is trapped. The strength of the field is assumed to grow in theradial direction $\sim $ $r^{4}$. Excited states of semi-vortex solitons havevorticities $S$ and $S+1$ in their two components, each being an eigenstate ofthe angular momentum. They are fully stable up to $S=5$. Excited state ofmixed-mode solitons feature interweaving necklace structures with oppositefractional values of the angular momentum in the two components. They arestable if they are built of dominant angular harmonics $\pm S$, with $S\leq 4$.Characteristics and stability of these two types of previously unknownhigher-order solitons are systematically analyzed. Their characteristic size is$\sim 10$ $\mathrm{\mu }$m, with the number of atoms $\lesssim 10^{5}$

Excited states of two-dimensional solitons supported by the spin-orbit coupling and field-induced dipole-dipole repulsion