I've set up multi-store with multi-domain, but I'm facing a weird issue that is default store is running perfectly but another store is not able to load CSS.
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Try to run these commands in your root installation folder using your SSH access:
alias mage="php -d memory_limit=-1 -f bin/magento" chmod -R 775 pub/static/ var/ pub/media/ && rm -rf var/view_preprocessed/ var/cache/ var/page_cache/ var/tmp/ var/generation/ pub/static/frontend/ ; mage deploy:mode:set developer; mage setup:upgrade && mage setup:db-data:upgrade && mage dev:source-theme:deploy && mage setup:static-content:deploy && mage cache:flush && mage indexer:reindex; chmod -R 775 pub/static/ pub/media/ var/
Have you assigned the theme to the new store? if so then have you redeployed the site also reindex the data and finally flushed the cache
php bin/magento setup:static-content:deploy en_GB en_US php bin/magento indexer:reindex php bin/magento cache:flush