Edraw can both export and import Visio drawings (.vsdx) just fine since version 7.7. You can then use the data in a new or already existing projects (.eddx). It is standard function in EDraw Max, no middle step exchange formats required.
Convert Microsoft Visio drawing to Edraw project.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert vsdx to eddx on Windows
A versatile diagramming program
Convert from vsdx file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.