This paper aims at providing a substantial step toward the global boundedness and blow-up of solutions to a two-species and two-stimuli chemotaxis model, in which the process of the species results in a short-ranged chemical signaling loop. More precisely, we consider the following Neumann initial-boundary value problem $$\begin{aligned} \left\{ \begin{array}{llll} u_t=\Delta u-\chi _1\nabla \cdot (u\nabla v), &{} \quad x\in \varOmega , &{}t>0,\\ 0=\Delta v-\mu _2+w, &{} \quad x\in \varOmega ,&{} t>0,\\ w_t=\Delta w-\chi _2\nabla \cdot ( w\nabla z)-\chi _3\nabla \cdot ( w\nabla v), &{} \quad x\in \varOmega , &{}t>0,\\ 0=\Delta z-\mu _1+u, &{} \quad x\in \varOmega , &{}t>0\\ \end{array} \right. \end{aligned}$$ in the unit disk $$\varOmega :=B_1(0)\subset \mathbb {R}^2$$ with chemotactic sensitivities $$\chi _1>0,\chi _2>0$$ and $$\chi _3\ge 0$$ and radially symmetric nonnegative initial data $$u_0$$ and $$w_0$$ , where $$\mu _1 and \mu _2$$ are given, respectively, by $$\mu _1:=\frac{m_1}{|\varOmega |}$$ and $$\mu _2:=\frac{m_2}{|\varOmega |}$$ with $$m_1=\int _{\varOmega }u_0$$ , $$m_2=\int _{\varOmega }w_0$$ . Explicit conditions on $$\chi _i, \mu _i$$ , $$u_0$$ and $$w_0$$ are given for the simultaneous global boundedness and simultaneous finite-time blow-up of classical solutions. Specifically, when the effect of $$\chi _3>0$$ is strong enough in the sense that the dynamical properties of the above system behave like one single-species Keller–Segel chemotaxis system, it is shown that if only the total mass $$m_2<\frac{4\pi }{\chi _1}$$ and $$m_2<\frac{4\pi }{\chi _3}$$ , the solutions are globally bounded, while blow-up may occur provided that $$m_2>\frac{4\pi }{\chi _1}$$ and $$m_2>\frac{8\pi }{\chi _3}$$ . Moreover, in view of the chemotactic signaling loop, one can find a critical mass phenomenon: with some finite time $$T>0$$ . The simultaneous blow-up phenomenon for two species is also given in this paper. This, in particular, shows, when $$\chi _3=0$$ , that smallness of mass of each species implies global solvability, whereas largeness of masses induces blow-up to occur.