<p>We consider a two-type reducible branching Brownian motion, defined as a particle system on the real line in which particles of two types move according to independent Brownian motions and create offspring at a constant rate. Particles of type 1 can give birth to particles of types 1 and 2, but particles of type 2 only give birth to descendants of type 2. Under some specific conditions, Belloum and Mallein showed that the maximum position <i>M</i>_<i>t</i> of all particles alive at time <i>t</i>, suitably centered by a deterministic function <i>m</i>_<i>t</i>, converge weakly. In this work, we are interested in the decay rate of the following upper large deviation probability, as <i>t</i> → ∞</p><p><Equation ID="Equa"> <EquationSource Format="TEX">\(\mathbb{P}(M_{t}\geq \theta m_{t}), \quad \theta &gt;1.\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mo stretchy="false">(</mo> <msub> <mi>M</mi> <mrow> <mi>t</mi> </mrow> </msub> <mo>≥</mo> <mi>θ</mi> <msub> <mi>m</mi> <mrow> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em" /> <mi>θ</mi> <mo>&gt;</mo> <mn>1.</mn> </math></EquationSource> </Equation></p><p>We shall show that the decay rate function exhibits phase transitions depending on certain relations between <i>θ</i>, the variance of the underlying Brownian motion and the branching rate.</p>