Improved thermomechanical properties have been reported for various high-entropy oxides containing typically five metal cations. This study further investigates a series of duodenary (11 metals + oxygen) high-entropy oxides by mixing different fractions of a five-cation fluorite-structured niobate and a seven-cation pyrochlore (both containing Yb) with matching lattice constants. Nine compositions of duodenary high-entropy oxides have been examined. All of them exhibit single high-entropy phases of either disordered fluorite or ordered pyrochlore structure. An order-disorder transition (ODT) is evident with changing composition, accompanied by a reduction in thermal conductivity (k). In comparison with the ODT criteria developed from ternary oxides, these duodenary oxides are more prone to disorder, but the ODT is still controlled by similar factors (but at different thresholds). Interestingly, there are abrupt increases in Young's modulus (E) at low mixing concentrations near both endmembers. The E/k ratios are increased, in comparison with both endmembers. This study suggests a new route to tailor high-entropy ceramics via controlling cation ordering vs. disordering.