We investigate the effect of weak interband impurity scattering on the intertype (IT) domain between type-I and type-II superconductivity in diffusive two-band superconductors. Our results show that the significant broadening of the IT domain with increasing band diffusivity ratio, previously established in the absence of interband scattering, persists under weak interband scattering. However, depending on the microscopic parameters, weak interband scattering can either slightly narrow or further expand the IT domain. Consistent with the case of negligible interband scattering, we identify two distinct IT regimes in the presence of weak interband scattering. The first variant (here referred to as IT-$\alpha$) has the upper boundary controlled by a sign change of the short-range vortex-vortex interaction, while the lower boundary is governed by a sign change of the long-range interaction. This ordering is reversed in the second variant, here referred to as IT-$\beta$. In both regimes, the vortex-vortex interaction is nonmonotonic: long-range repulsive and short-range attractive in the IT-$\alpha$ domain, and short-range repulsive and long-range attractive in the IT-$\beta$ regime. We also find that weak interband scattering tends to suppress the IT-$\alpha$ regime in favor of IT-$\beta$. Our findings establish the stability and tunability of the intertype regime in dirty multiband superconductors, which is crucial for harnessing its unique magnetic properties.

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• Impurities in superconductors
• Multiband superconductivity
• Phase diagrams
• Vortices in superconductors
• Superconductors
• Type-I superconductors
• Type-II superconductors
• Methods in superconductivity