Yes, SymmetricDS can certainly do this! As described in this official tutorial, you would need to set up Bidirectional replication:
Download and review official documentation on how to install (Un-Zip).
Copy 2 sample files (corp-000.properties and store-001.properties) from the "samples" sub-directory into the "engines" sub-directory.
Review official documentation on how to edit engine files.
Edit engines/corp-000.properties to connect node to SQL Server.
Edit engines/store-001.properties to connect node to MySQL.
Review group assignments of nodes and group links.
Prepare to register store-001 node with with corp-000 using the registration.url property in the engine file.
Configure test table for replication - on both databases.
Start SymmetricDS! (use the bin/sym script at first, later you can run it as a service)
Review logs and sym_outgoing_batch table for new entries.
Comment of this answer to refine it and help community!
And, if you have a different database or use case, please open a new question with the [symmetricds] tag attached.