There is no straightforward answer to your question, all depends on the sediment conditions in suspension and in the river bed. For instance, when a river is heavily loaded with suspended mud (there is no such thing as a predictable “maximum”), the maximum erosion velocity of a sandy bed is hindered by the reduced penetration velocity of water-mud mixture to dilate of the grain packing necessary for erosion from the bed. On the other hand, a high suspended sediment concentration reduces the difference of the bulk sediment density of the bed with the overlying fluid, which in case of a bed that consists of cohesive material, or silt, may enable large pieces of the bed to be ripped off and carried away with the flow while disintegrating. A nice example of this is the Yellow River (see Van Maren, D.S., Winterwerp, J.C., Wang, Z.Y., Pu, Q. (2009) Suspended sediment dynamics and morphodynamics in the Yellow River, China. Sedimentology, 56 (3), pp. 785-806).

Thanks a lot Richard, However, in case of sudden overload provided to the river channel by this or that reason ( Heavy mass wasting... etc. in upstream ) channel is overloaded near about choked, it is therefore, limitations on channel load movement that lead to stall/ slow  the erosion.