Adjust the second animation's Animation Repeat value if necessary.
Open the Strip Settings for the second animation strip and note its exact Start Frame.
Open the settings for the first displacement strip (created in step 4). Enable Custom Action Frame Range. Modify its End Frame to end one frame before the second animation strip's start frame noted in step 7.
Create a second displacement strip (as explained in step 4) for the second animation. Set its Start Frame to match the second animation's start frame. Ensure it starts at the correct position relative to where the first displacement ended by using the Calculate Linear Offset operator in the modifier settings. You may also need to set this second displacement strip's Blend Type to Replace if the previous displacement strip used Hold Forwardextrapolation.
Adjust frame ranges and timing as needed across all strips.
Splitting/Refining Existing Strip Animation
Select the strip (can be editable or non-editable) containing the animation you want to split/refine.
In Pose Mode, select the bones whose animation you want to isolate (e.g., arm bones, head bone).
Click the Copy Animation from Selected Bones operator, and enable the Extract Animation from Original setting. This removes the animation for the selected bones from the source strip (and its underlying action) and places it into the new strip. If you leave this setting unchecked, the animation for the selected bones will exist in both the original and the new strip (effectively duplicating it), which is usually not the desired outcome for splitting.
A new editable strip (and a new action) is created containing only the animation for the selected bones.
You can now independently adjust the Influence, Timing, Speed, or even replace the animation entirely in the new strip, without affecting the original strip's animation for the other bones. You could also mute (Mute Strip) the new strip entirely to remove that part of the animation non-destructively.
Repeat steps 1-6 if you want to isolate more bone groups into separate strips.