Low-degree　coefficients　of　time-variable　gravity　field　models　from　Gravity　Recovery　and　Climate　Experiment　(GRACE)　and　GRACE-Follow　On　(GRACE-FO)　capture　large-scale　mass　changes　within　the　Earth　system.　However,　some　of　these　coefficients　are　either　missing　(e.g.,　degree-1　coefficients)　or　poorly　determined　(e.g.,　(Formula　presented.)).　Such　a　situation　is　exacerbated　particularly　over　the　GRACE-FO　period　when　one　of　the　accelerometers　carries　elevated　noise.　In　this　study,　we　present　a　framework　for　estimating　low-degree　coefficients　using　the　fingerprint　approach.　Our　results　demonstrate　that　this　method　can　reliably　estimate　multiple　coefficients　simultaneously,　producing　degree-1,　(Formula　presented.),　and　(Formula　presented.)　estimates　that　are　comparable　to　the　currently　recommended　solutions,　both　in　direct　comparisons　and　in　the　context　of　estimating　mass　changes　over　the　Antarctic　Ice　Sheet.　This　framework　not　only　provides　an　alternative　approach　for　determining　low-degree　coefficients　currently　identified　as　problematic　in　GRACE/GRACE-FO　gravity　field　models,　but　also　shows　potential　for　addressing　other　degraded　low-degree　coefficients　that　may　emerge　during　future　GRACE-FO　operations.　©　2025.　American　Geophysical　Union.　All　Rights　Reserved.