Docker-compose.yml file that builds a base image, then children based on it?

Yes, kind of. Use it like this:

version: '2'

services:

    wls-admin:
        container_name: wls-admin
        image: weblogic-domain
        build:
            context: wls-admin
            args:
                - ADMIN_PORT=${WLS_ADMIN_PORT}
                - CLUSTER_NAME=${WLS_CLUSTER_NAME}
                - PRODUCTION_MODE=dev
        networks:
            - wls-network

image clause here makes docker-compose build generate docker image named weblogic-domain for this service. This image can be re-used by other services’ Dockerfiles, even in the same build process.