Searching mass-balance analysis is applied to find possible standard oxide composition distributions of Martian blueberries (hematite-rich spherules). This found three groups of complete solution sets to the mass-balance equations consistent with the non-detection of silicates in blueberries (by NASA’s rover Opportunity). Two of these groups were previously unknown. One of the groups has blueberry (standard oxide) distributions nearly identical to one found in 2006, with 99.7 wt% FeO/Fe2O3, 0.3 wt% Ni, and zero content for other oxides. Two of ten investigations found a very small group with composition intermediate to the others. The largest group of 152, 501 complete solution sets have blueberry distributions with average iron oxide content of 91.2 (+/-2.9) wt% and Ni content of 0.30 (+/-0.06) wt%. The main distinguishing feature between the groups is that the blueberry distributions of the largest group have five oxides/elements (MgO, P2O5, Na2O, SO3, and Cl) with a collective, summed weight percentage that averages 6.7 (+/- 2.2) wt%. This result is robust to changes in an SiO2 cut-off that determines inclusion/exclusion in the larger group. Searches over spaces of filtering distributions of basaltic and dusty soils were a methodological advance. The results significantly narrow the possible range of iron oxide weight percentage in blueberries from the conclusions of previous major papers concerned with blueberry composition. The allowed levels of iron oxide are so high, and top, loose blueberries are so plentiful, that blueberries are an attractive source material to start the construction of steel infrastructure for science on Mars.