<p>Shape quantum phase transitions are an important topic in nuclear structure. In this paper, we investigate the finite-<i>N</i> shape quantum phase transition in the SU3-IBM. In this newly proposed framework, a sphere-like <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-soft spectrum is identified to address the long-standing puzzle of apparently spherical nuclei, and it represents a distinct <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-soft rotational mode. In this paper, the shape phase transition along the new <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-soft line is examined first, and the neighboring case on the prolate side is then analyzed. Some diagnostic observables are examined. We show that double shape phase transitions occur along a single parameter path. The new <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-softness is demonstrated to be a shape phase, and the shape phase transition from the new <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-soft phase to the prolate shape is identified. Experimental indications are also identified, and <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(^{108}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>108</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Pd may be a candidate critical nucleus.</p>