Described apparatuses and methods relate to adaptive refresh staggering for a memory system that may support a nondeterministic protocol. To help manage power-delivery networks in a memory system, a memory device can include logic that can be programmed to stagger the start of refresh operations for each die upon receiving a command to enter a lower-power mode, such as self-refresh. The staggered start can be implemented at a channel level, a package level, or both. The programming sets a delay for each die so that initiation of refresh operations is staggered. Thus, a first die can initiate refresh operations when a command to enter the lower-power mode is received (e.g., approximately zero delay). However, initiation of refresh operations for subsequent dies (e.g., “after” the first die) is delayed, which can reduce peak current draw and power consumption.