Assuming you already have rustup with a (stable or beta) toolchain installed, the following list of shell commands will get you a fresh homebrewed Rust toolchain.

git clone
cd rust
# switch branch here at will !

# This builds the extended rust for your machine using your local rust.
./configure --enable-extended --tools=rsl,rustmft,src --prefix=~/.local --enable-local-rust
./ install

# This makes rustup aware of your toolchain
rustup link myrust $HOME/.local

# builds rust for the specified targets but skips docs
./configure --disable-docs --prefix=~/.local --enable-local-rust
# We might for fun add here more targets such as msp430 or avr
# There may be a way to directly install the newly built targets but I couldn't find it
./ dist --target=thumbv7em-none-eabihf,thumbv7em-none-eabi,thumbv7m-none-eabi,thumbv6m-none-eabi
pushd build/dist
for f in $(ls rust-std*.tar.xz); do tar xf $f; done
for d in $(ls -d rust-std*/); do pushd $d; ./ --prefix=$HOME/.local; popd; done

You can even rustup default myrust if you dare!