In case your objective is to go to dynamics 365 onprem, the standard process is to move your DB/DBs step by step through CRM major builds (using last cumulative updates for each major build) and open support tickets if you face problems.
- 4.0->2011->2013->2015->2016/365->v9.1
One of the problems you may face with support is that crm 2011 and crm 2013 are out of support, so this is a topic sensible to interpretation. But because your final goal is to move to a supported version, we will surely do a best effort.
If the objective is to go Dynamics online, as shared by Leah, the best approach is to engage fasttrack and see what the feedback is.