Several series of A/SnO2 and Mn/B multilayers, where A and B are thin layers (0.4-10.1 nm) of SnO2, SiO2, Si, Al, Mn, or MnOx, have been investigated magnetic, electronic, and structurally. The study demonstrates that the detected ferromagnetism is related to regions of high density of defects in SnO2 induced by doping under particular conditions. The observed room-temperature ferromagnetic (RTFM) signal does not scale to Mn content but increases with the number of interfaces and their roughness. The presence of Mn in 3+ oxidation state in the SnO2 lattice is a necessary condition but is not enough to promote ferromagnetism which also requires the presence of Sn2+. The high oxygen deficiency induced by Mn doping in the tin-oxide layers is mostly compensated by the formation of the stable SnO phase. Moreover, the RTFM signal decreases upon annealing either in O-2 rich or in vacuum atmospheres. The combination of Mn with SiO2, Si, or Al produces paramagnetic signals but no ferromagnetism; consequently SnO2 is a crucial ingredient of this RTFM. The observed ferromagnetism may be explained by short-range ferromagnetic correlations between Mn probably mediated by induced holes at oxygen sites of SnO2 in the vicinity of trivalent Mn3+ doping ions. The inhomogeneous Mn distribution inside tin oxide at the multilayer interfaces may produce large enough regions with high defect concentration to allow long-range ferromagnetic order. All undoped SnO2 films, grown in a wide set of different conditions, show paramagnetic signals with high-J values but no ferromagnetism is detected probably because of the high density of defects required to establish a ferromagnetic order based in a short-range mechanism.