Signing Assets using productsign and codesign

Hi,

I am currently using both productsign, codesign tools for signing assets. Example of simple commands are:

# Unlock keychain
security unlock-keychain -p ${keychain_name} ${keychain_name}.keychain

# Code sign
codesign --keychain ${keychain_base_path}/${keychain_name}.keychain --sign ${codesign_identity_name} ${app_file}

# Product Sign
productsign --keychain ${keychain_base_path}/${keychain_name}.keychain --sign ${pkgsign_identity_name} "${pkg_file}" "${output_file}"

# Lock keychain
security lock-keychain ${keychain_name}.keychain

I am running a SpringBoot application that is listening for signing requests, and runs a bash script with these commands above. My question, if the spring app is multithreaded, is it possible to run these commands in. parallel? So that many files can be signed at the same time? Or is it only possible to sign sequentially?

Thanks