It houses unique archive material, rare manuscripts, artwork, photographs, books and original sound recordings, but only 140 out of 950 artefacts are currently on display.
"BBC 7's fresh on-air sound and its addictive mix of archive comedy, drama and books is proving a great hit with our listeners, " said head of programmes Mary Kalemkerian.
One proposal is to give regulators the power to go through the books of the biggest providers and challenge them to prove their business models are sound.