README These are raw data for the Figs.1-2, 4-6, and Supplementary Figs. S1-S5, S7-S11 in the Supplementary Material for this work. Please see our paper for detailed descriptions and discussions. Figure1_SourceData.xlsx: XRD patterns of the synthesized multi-RE-principal-component RE2Si2O7 samples. Figure2_SourceData.xlsx: Data of Rietveld refinement on room-temperature XRD patterns for the studied materials. Figure4_SourceData.xlsx: The average RE3+ radius and the deviations for multi-RE-principal-component RE2Si2O7 compounds. Figure5_SourceData.xlsx: Statistical parameters for the Gaussian-fitted mixing energy distribution spectrum for all ensembles. Figure6_SourceData.xlsx: The calculated configurational entropy of mixing for each configuration ensemble. FigureS1_SourceData.xlsx: XRD patterns of the synthesized multi-RE-principal-component RE2Si2O7 samples belonging to the category I. FigureS2_SourceData.xlsx: XRD patterns of the synthesized multi-RE-principal-component RE2Si2O7 samples belonging to the category II. FigureS3_SourceData.xlsx: XRD patterns of the synthesized multi-RE-principal-component RE2Si2O7 samples belonging to the category II but showing sluggish beta-to-gamma polymorphic transformation. FigureS4_SourceData.xlsx: XRD patterns of the synthesized (REIx1REIIx2REIIIx3REIVx4)2Si2O7 (x1+x2+x3+x4=1) samples belonging to the category III. FigureS5_SourceData.xlsx: Rietveld refinement of room-temperature X-ray diffraction (XRD) patterns for the YHoTmLu and TbErYbLu systems. FigureS7_SourceData.xlsx: The interatomic force constant and bond length of RE-O and Si-O bonds in beta-(Er0.25Tm0.25Yb0.25Lu0.25)2Si2O7 and beta-RE2Si2O7 (RE = Er, Tm, Yb and Lu) lattices. FigureS8_SourceData.xlsx: XRD patterns of the synthesized equimolar and non-equimolar multi-RE-principal-component RE2Si2O7 compounds. FigureS9_SourceData.xlsx: The calculated distribution of formation energy for all the metastable configurations in the studied ensembles, together with the Gaussian fitting. FigureS10_SourceData.xlsx: Results of convergence test on the size of beta-type and gamma-type (Dy0.25Ho0.25Yb0.25Lu0.25)2Si2O7 configuration ensembles. FigureS11_SourceData.xlsx: Results of the convergence test on the energy cut-off in DFT calculations.