Hi sherlan ,
I see two ways to generate a nested MSO.
1. Anchor an existing MSO to a text frame in a state of an MSO.
That's not the solution to your animation problem.
2. Add a new generic MSO to a graphic frame in a state of an MSO.
That only can be done by scripting. It will create a generic, two-state MSO inside a graphic frame.
Case 2 will not work with anchored objects so the animation will play if added to a state of the nested MSO.
However that means you will have to recreate all other aspects of your predefined MSO you are currently using.
Here a Publish Online document where I am showing a MSO inside a MSO that contains several animations in several states:
https://indd.adobe.com/view/606bc199-2f8e-4037-b200-8d98577f902e
Initial state: One MSO ( you see the blue state 1 with a button to click to the next state ) and one animation of a magenta rectangle on the page.

The button in state 1 of the MSO leads to state 2 of the MSO where another MSO is nested inside.
And that nested MSO is showing an animation in every state of its 3 states. You can click through the 3 states with the button above the nested MSO:

Regards,
Uwe