Unfortunately no. Only one Develop Setting can be saved to a dng file.

However you have 2 options to export the Image and its Virtual Copies out of your Lightroom catalogue.

Option 1

Select your whole Stack, and click on the Export-Button in the library module. Select the "export as dng" Preset.

Now Lightroom creates a separate .dng file for each of your virtual copies, which can be processed by Photoshop or another tool.

Option 2

Put the images you want to export into a collection or simply select the folder where they are stored. Now do a right click and select "Export as catalogue". Lightroom will create now another catalogue, and just export one .dng for each master file. You now can import that whole catalogue into another Lightroom catalogue (possibly on another machine), and you will get back your virtual copies.

E.g. You have your Catalogue called "Master", from there you select one dng with 3 virtual copies. Now export it to another folder with the name "temporary". Lightroom will create a .lrcat file and copy the dng to it.

Now you can open your second Catalogue (for simplicity called "second"), and then go to "File > Import from another catalogue". Then select the temporary .lrcat file, and Lightroom asks you some questions about storing the imported files. After the import finishes, your master dng and all its 3 virtual copies are in your second catalogue.

Please be aware that all collections from "Master" catalogue will be copied as well.