||A recent reinvestigation of the alloy system CeIn3-xSnx between the antiferromagnetic (AF) Kondo-lattice CeIn3 and the intermediate valent CeSn3 has shown that the AF order disappears at a quantum critical point (QCP) at x(c) approximate to 0.65. Preliminary evidences for a first order transition below T-N at x < x(c), indicating a complex magnetic phase diagram, have motivated the present detailed investigation of specific heat and resistivity on fine tuned samples in the 0.25 less than or equal to x less than or equal to x(c) range. These results confirm the first order transition at T-I < T-N in a reduced concentration range (0.25 < x < 0.47) and suggest that the phase boundary T-I (x) merge with the T-N(x) near x approximate to 0.37, leading to a tetracritical point. A similar first order transition was previously observed in the CeCu2(Si,Ge)(2) system at low Ge-concentration. Since in this alloy the first order transition also appears in the vicinity of a QCP, the question arises concerning how general this property is at AF critical points in Ce-based alloy systems.