Can a Dockerfile extend another one?

Using multi-stage build is definitely one part of the answer here.

docker-compose v3.4 target being the second and last.

Here is a example to have 2 containers (1 normal & 1 w/ xdebug installed) living together :

Dockerfile

FROM php:7-fpm AS php_base 
ENV DEBIAN_FRONTEND noninteractive

RUN apt-get update && \
    apt-get install -y git libicu-dev libmagickwand-dev libmcrypt-dev libcurl3-dev jpegoptim
RUN pecl install imagick && \
    docker-php-ext-enable imagick

RUN docker-php-ext-install intl
RUN docker-php-ext-install pdo_mysql
RUN docker-php-ext-install opcache
RUN docker-php-ext-install mcrypt
RUN docker-php-ext-install curl
RUN docker-php-ext-install zip

FROM php_base AS php_test

RUN pecl install xdebug 
RUN docker-php-ext-enable xdebug

docker-compose.yml

version: '3.4'

services:
  php:
    build:
      context: ./
      target: php_base

  php_test:
    build:
      context: ./
      target: php_test
  
# ...