I'd suggest to open a support case for this with Dynatrace Support
I hadn't heard of MicroFocus diagnositics until now, but it looks like it supports older technology stacks for profiling Java and .NET with an agent (they call it a probe). You might need to reach out to Microfocus support to understand if they will support other agents? In theory, it's sometimes possible, especially for Java because it has the concept of either Java (JVM) agent or Native code agent, so the instrumentation / introspection methods could differ substantially.
However the last product release MF had for Diagnostics looks to be around 3 years ago and they support obsolete software like Internet Explorer - so even with the support offered, I'd personally be wary of any product improvement potential to address this use case of running two agents. In my opinion, it may well be an unsupported setup.
Most likely it won't work together if deep monitoring is in question. If you considering OneAgent in infrastructure mode, then it will work definitely.
But MF diagnostic is a legacy tool, I recommend replacing that with Dynatrace 🙂
In general Dynatrace does not support co-existence with other native/java agents. Most of them are closed source and it is unknown how they work, which could lead to severe side effects. Usually the automatic injection removes all known conflicting agents to avoid crashes and such.