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It was revealed in our previous studies that there exists a maximal possible accretion rate for slim discs with constant accretion rates because the correctly calculated vertical gravitational force can only gather some limited amount of accreted matter. Here we show that when the accretion rate is not constant and instead decreases with decreasing radius because of outflows, such that the amount of accreted matter is adjusted to be within the allowed limit, global slim disc solutions can be constructed even for the case that accretion rates at large radii apparently exceed the maximal possible value. This result further demonstrates that outflows seem to be unavoidable for accretion flows with large accretion rates at large radii.