combinations of $\rho^1$ and $\rho^2$ in the allowed ranges. For example, with $U_{12}= 0.4U$ and for $\mu/U=0.2$, $J/U=0.01$ we observe $0.33\lesssim \rho^1\lesssim 0.7$. In the figure, the half filling lobe $\rho^k = 0.5$ and $\rho = 1$ at $J/U=0$ lies in the domain $0\leqslant\mu/U \leqslant 0.4$. In general, in the miscible domain, the half filling lobe $\rho =1$ at $J/U=0$ lies in the domain $0\leqslant\mu/U \leqslant U_{12}/U$. The other MI lobes with higher $\rho$ occur at the higher values $\mu/U$. In general, the MI lobes have $\rho=n$ with $n\in\mathbb{N}$ and $\rho^k = n/2$. Thus, for MI lobes with odd $n$ the average occupancy of each species is half integer.

With increasing $U_{12}$ the MI lobes with odd integer occupancies grows in size, but the size of MI lobes with even integer occupancies remain the same till $U_{12}=U_{kk}$ but shifts to higher $\mu/U$. This can be understood from Eq. (\[order\_par\_ana\]). The trend is discernible from the phase diagrams in Fig.\[tbec\_ph\](b-c). This, in the case of weakly interacting TBECs, is equivalent to a march towards phase separation [@ho_96; @ao_98; @gautam_11; @roy_15_2; @bandyopadhyay_17]. For $U_{12}>U_{kk}$, the criterion for phase separation, the size of the MI lobe $\rho =2$ is different. But, once the 