Paper 62BB develops the many-body and non-spherical source-law checkpoint in the Holosphere gravity sequence. Earlier papers established the isolated spherical branch, including weak exterior recovery, second-order Schwarzschild coefficient closure, source-length calibration, conservation consistency, perturbations, weak rotation, and strong-field readability. Paper 62BB asks the next source-geometry question: how Holosphere gravity should treat sources that are not isolated, not spherical, or not weakly separated. The central source law is the Holosphere weak static support-source equation: the support burden B_source is sourced by the support-source density rho_H. The familiar isolated result B_source = mu_H/r is recovered only when the source is compact, spherical, exterior, readable, and free of leading many-body or non-spherical corrections. In that case, mu_H is the integrated support-source length, calibrated in the weak branch as mu_H = GM/c^2. Paper 62BB generalizes this isolated result. For non-spherical sources, the exterior burden must include support multipoles. The monopole term mu_H/r is only the first term. Higher angular structure appears through dipole, quadrupole, and higher multipole coefficients, depending on the support-source density rho_H(x). A non-spherical source cannot be treated as a pure monopole unless the higher multipoles are absent or subleading. For many-body systems, Paper 62BB separates weak superposition from corrected source behavior. In the weak separated-source branch, the total source burden is approximately the sum of the individual burdens, up to higher-order corrections. This requires weak burdens, small support-domain overlap, subleading interaction terms, subleading correction terms, and open readability. If these conditions fail, the source law must include interaction burden, support-overlap burden, and correction burden. The paper also keeps conservation and readability attached to the source law. General source geometry must remain compatible with the divergence-safe tensor source ledger. If multipoles, overlaps, interactions, or correction channels are active, they must be declared rather than hidden inside a monopole or simple superposition formula. If readability fails, the ordinary source-metric branch is not assigned. The result is bounded. Paper 62BB does not solve the full relativistic many-body problem, numerical relativity, strong-field binary mergers, radiation reaction, waveform generation, or fully nonlinear matter coupling. Its contribution is the source-law hierarchy needed before final GR-limit synthesis: monopole sources, multipole sources, many-body weak superposition, overlap-corrected sources, conservation checks, correction channels, and readability gating.