<p>Previous investigations of the three-body dynamics of <i>B</i> mesons have shown that no Efimov effect arises in systems composed of three <i>B</i> and <i>B</i>^* mesons. This implies that the properties of such three-body systems can be described reliably within nonrelativistic effective field theory (NREFT) with short-range interactions using only two-body input, as three-body forces are strongly suppressed. In this work, we present leading-order predictions for the three-body point production rates of systems consisting of three <i>B</i> and <i>B</i>^* mesons. These predictions provide a novel way to experimentally probe the <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi>B</mi> <mfenced close=")" open="("> <mo>∗</mo> </mfenced> </msup> <mo>−</mo> <msup> <mover accent="true"> <mi>B</mi> <mo stretchy="true">¯</mo> </mover> <mfenced close=")" open="("> <mo>∗</mo> </mfenced> </msup> </math></EquationSource> <EquationSource Format="TEX">\( {B}^{\left(\ast \right)}-{\overline{B}}^{\left(\ast \right)} \)</EquationSource> </InlineEquation> interactions, which play a crucial role in the hadronic-molecule interpretation of the <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>T</mi> <mrow> <mi>b</mi> <mover accent="true"> <mi>b</mi> <mo stretchy="true">¯</mo> </mover> <mn>1</mn> </mrow> </msub> <mfenced close=")" open="("> <mn>10610</mn> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( {T}_{b\overline{b}1}(10610) \)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>T</mi> <mrow> <mi>b</mi> <mover accent="true"> <mi>b</mi> <mo stretchy="true">¯</mo> </mover> <mn>1</mn> </mrow> </msub> <mfenced close=")" open="("> <mn>10650</mn> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( {T}_{b\overline{b}1}(10650) \)</EquationSource> </InlineEquation> states. Moreover, they provide a way to test the approximate conformal symmetry predicted for such systems at low energies experimentally.</p>