'crosstool-ng gcc builtin paths

I have built a cross compiler, and am planning to use it with a local sysroot.

The target uses the exact same versions of binutils. glibc as the built cross compiler.

I can compile and run programs but I have to specify an extra library search path for libgcc_s.so

aarch64-rpi4-linux-gnu .... --sysroot /mnt/rpi_rootfs -L  /mnt/rpi_rootfs/usr/lib/gcc/aarch64-linux-gnu/10 ....

On the target, this is not required, as the search path is correct:

gcc -print-search-dirs
.... /usr/lib/aarch64-linux-gnu/10/ ....

Crosstool-ng generated a sysroot with sysroot/lib/libgcc_s.so

Is it possible to specify extra 'builtin' search paths in the crosstool-ng configuration?
Can I somehow update the gcc builtin search paths of the generated cross compiler?

gcc arm64 crosstool-ng

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