If anyone has experienced engine crashes when adding a new parameter to an anim graph, this is likely the fix:
EMFX has a hardcoded assumption that an anim graph is already loaded into it when it starts up. If EMFX is opened via the tools menu, or the window is opened when the editor starts up, no anim graph is loaded at those times. When you add one, it will still believe none has been loaded and it will crash when adding a new parameter. The save button in EMFX will also be greyed out if this is occurring, though you can still save through the file menu drop down option.
The workaround is to open EMFX from a populated anim graph component on an outliner entity. Make sure you close the window before opening it in this way.