Storing rhymes with:
restoring, restoring, adoring, boring, deploring, doehring, doring, exploring, flooring, goehring, goring, ignoring, imploring, kohring, loring, moehring, mohring, moring, outpouring, outscoring, poring, pouring, restoring, roaring, scoring, shoring, snoring, soaring, underscoring, warring
Storing sounds like:
saturn's, saturns, sauternes, scattering, sequestering, shattering, shoestring, shuddering, shuttering, sidearms, sistrunk, southern's, squadrons, staring, starnes, starns, starring, stearns, stearns's, steering, stern's, sternness, sterns, stirring, stirrings, storm's, stormes, storminess, storming, storms, straining, strains, strang, strange, strangis, strangwayes, stransky, straying, streaming, streams, streng, strenuous, string, strings, stringy, stronach, strong, strumming, strums, strung, strunk, strunk's, sturmans, stuttering, suturing