Flow-driven electromagnetic instabilities play a critical role in various space plasma environments. Utilizing linearized Vlasov–Maxwell model equations, this paper examines the dispersion relations of drifting Alfvén waves under the influence of temperature anisotropy. The study identifies significant modifications in the combined drifting Alfvén modes compared to previous research. The positive (P) and negative (N) solutions, which represent coupled flow-driven Alfvén modes, reveal threshold values for normalized streaming velocity, demarcating the transition between real and imaginary frequency spectra, and emphasize the impact of ion temperature anisotropy. The analysis discusses the role of fast-moving ions in developing instability, considering the effects of density ratios and streaming velocities. When the densities of interpenetrating plasmas are equal and the merging point ωs+f of the solutions is identified, the influence of ion temperature anisotropy on the P-N Alfvén modes is particularly notable in different low plasma beta regions. However, for fixed ion streaming velocities, varying densities and ion temperature anisotropy in the range T∥>T⊥ cause the modes to become finite forward while they become infinitely forward when T∥<T⊥. This investigation provides insights into the behavior of Alfvén waves in interpenetrating plasmas and sheds light on electromagnetic wave instability mechanisms in such interpenetrating plasmas.