There should be no issues using our current LTI 1.1 keys-based process to support multiple Learning Management Systems (LMS) on the same license. There are no limitations to the number of platforms used, so long as all of the learners acciessing the LMS are enrolled students and covered under your university's Campus-Wide License. You can use the same LTI keys in multiple LMS platforms from different vendors, or in different contexts (development, staging, test, and production) on the same platform.
The implementation process for MATLAB Grader is slightly different for each LMS, and MathWorks will need to know in advance whether each LMS has a different LMS admin (the person who will be logging in to generate/access their own LTI keys) or if a single person at the university will be performing the implementation for all LMS platforms. If it is multiple people, they will all need to be added as authorized admins to the license so that they can generate their own keys. Please contact your account representative, or contact Customer Support for assistance in adding LMS admins to your license.
From an instructor perspective, as long as they are logging into their MathWorks account when prompted on the first use of the tool in a new LMS context, they will have access to all of the content they build for courses that ran in the other LMS platforms. When this is done, we are able to tie content ownership back to the MathWorks account of the instructor user. While this is an optional step for instructors, it is very helpful when accessing multiple LMS platforms, or even teaching at multiple colleges/universities that have MATLAB Grader integrated into their LMS platform(s).