Building upon three late-type galaxies in the Virgo cluster with both a predicted black hole mass of less than ∼105 M o˙ and a centrally located X-ray point source, we reveal 11 more such galaxies, more than tripling the number of active intermediate-mass black hole candidates among this population. Moreover, this amounts to a ∼36 8% X-ray detection rate (despite the sometimes high, X-ray-absorbing, H i column densities), compared to just 10 5% for (the largely H i-free) dwarf early-type galaxies in the Virgo cluster. The expected contribution of X-ray binaries from the galaxies' inner field stars is negligible. Moreover, given that both the spiral and dwarf galaxies contain nuclear star clusters, the above inequality appears to disfavor X-ray binaries in nuclear star clusters. The higher occupation, or rather detection, fraction among the spiral galaxies may instead reflect an enhanced cool gas/fuel supply and Eddington ratio. Indeed, four of the 11 new X-ray detections are associated with known LINERs or LINER/H ii composites. For all (four) of the new detections for which the X-ray flux was strong enough to establish the spectral energy distribution in the Chandra band, it is consistent with power-law spectra. Furthermore, the X-ray emission from the source with the highest flux (NGC 4197: L X ≈ 1040 erg s-1) suggests a non-stellar-mass black hole if the X-ray spectrum corresponds to the "low/hard state". Follow-up observations to further probe the black hole masses, and prospects for spatially resolving the gravitational spheres of influence around intermediate-mass black holes, are reviewed in some detail.