Constraints on the number and luminosity of the sources of the cosmic neutrinos detected by IceCube have been set by targeted searches for point sources. We set complementary constraints by using the 2MASS Redshift Survey (2MRS) catalogue, which maps the matter distribution of the local Universe. Assuming that the distribution of the neutrino sources follows that of matter we look for correlations between `warm' spots on the IceCube skymap and the 2MRS matter distribution. Through Monte Carlo simulations of the expected number of neutrino multiplets and careful modelling of the detector performance (including that of IceCube-Gen2) we demonstrate that sources with local density exceeding $10^{-6} \, \text{Mpc}^{-3}$ and neutrino luminosity $L_{\nu} \lesssim 10^{42} \, \text{erg} \, \text{s}^{-1}$ ($10^{41} \, \text{erg} \, \text{s}^{-1}$) will be efficiently revealed by our method using IceCube (IceCube-Gen2). At low luminosities such as will be probed by IceCube-Gen2, the sensitivity of this analysis is superior to requiring statistically significant direct observation of a point source.