We are presenting our ongoing Lattice QCD study on $B - \bar{B}$ mixing on several RBC/UKQCD and JLQCD ensembles with 2+1 dynamical-flavour domain-wall fermions, including physical-pion-mass ensembles. We are extracting bag parameters $B_{B_d}$ and $B_{B_s}$ using the full 5-mixing-operator basis to study both Standard-Model mixing as well as Beyond the Standard Model mixing, using a fully correlated combined fit to two-point functions and ratios of three-point and two-point functions. Using 15 different lattice ensembles we are simulating a range of heavy-quark masses from below the charm-quark mass to just below the bottom-quark mass.