If you will plan well then you should be fine.
Key things in planning:
URL management: You should build system so that old URLs should redirect to respective new ones. At least for those pages where you have a good ranking.
If your new system can have as good or better user experience with similar content then you should be fine.
Let's understand by example:
Pages on Old CMS
Pages on New CMS
Now, you should try to have similar or better user experience on the new site.
- Load Time
- Content Placement
- Photos, Videos etc
And importantly, your old URLs must redirect (301) to respective new ones. Example:
example.com/inner-1 => example.com/web-inner-1
example.com/inner-2 => example.com/web-inner-2
If the planning may not be right then there will be maximum chances of the drop in ranking.