For the last few decades, researchers have been intrigued by multipolar ordering phenomena and related quantum phase transitions in heavy-fermion Kondo systems. However, a criticality induced by substitution level (x), temperature (T), or magnetic field (B) is poorly understood even in the prototypical material, Ce1-xLaxB6, despite a large collection of experimental results is available. In this work, we present T-B, x-T, and x-B phase diagrams of Ce1-xLaxB6 (B parallel to [110]). These are completed by investigating heat capacity, magnetocaloric effect (MCE), and elastic neutron scattering. A drastic increase of the Sommerfeld coefficient gamma(0), which is estimated from the heat capacity down to 0.05 K, is observed with increasing x. The precise T-B phase diagram including a high-entropy region is derived from the MCE analysis in which a knowledge beyond the equilibrium thermodynamics is involved. Finally, the x-B phase diagram at T = 0, which supports the existence of a quantum critical point at x > 0.75, is obtained by the same analysis. A detailed interpretation of phase diagrams strongly indicates positive correlation between the fluctuating multipoles and the effective electron mass.