If you want to use the multiarch approach for transparent emulation using QEMU, you need to find a distribution which supports all the architectures you’re interested in (your native architecture, and directly-supported alternate architecture you want, and the architectures you want to emulate). You can’t mix and match distributions (e.g. Raspbian for armhf and Debian for i386) because multiarch requires that packages installed for multiple architectures be installed with exactly the same version on all architectures.
Switching to another distribution would make this easier (assuming the distribution itself is a nice match for your Raspberry), but there may be another solution — it should be possible to use debootstrap to install another distribution with a foreign architecture in a chroot on your Raspberry, and use that to run binaries... I’ve used transparent emulation with multiarch, and foreign architectures with debootstrap, so I know the various components work, but I’ve never tried combining them so that’s left as an exercise for the reader.