EMT run shared by two panels

[Smith333]

I have a 200 amp service panel and a 100 amp subpanel. The neutral bonding screw in the subpanel is removed. I'm running some new EMT in the basement from the subpanel for some new outlets. The layout affords me the opportunity to also use this new EMT to extend a lighting circuit in an existing EMT run from the main panel. Each circuit will have a dedicated neutral from its respective panel, but obviously the grounds will be shared. Are there any problems with this?