Wine inside an AppImage: can I enable 32-bit architecture for 64-bit apps?

Wine requires 32-bit libs in order to run, even if I'm trying to run a 64-bit Windows application. I've gotten my Wine application working perfectly in an AppImage, except it needs libc6:i386 to be installed on the local machine (which kind of defeats the purpose of having one app that "just works").

I'm wondering if I can bundle libc6:i386 into the appimage itself. So far I've had no such luck. Copying in the files from the package into the appimage still leaves me with:

```
./bin//myapp: line 4: ../bin/wine: No such file or directory
```

(^ Classic error message when architecture of the file isn't supported)

If anyone has ideas I'd appreciate it. Been stuck on this for hours.