Currently, there is no option to get child terms of multiple parent terms. There is a 'parent' parameter that returns child terms of only one parent term.
There is a 'post_parent__in' parameter for 'WP_Query' and 'get_posts()' to get child posts of multiple parent posts, but there is no similar parameter for 'WP_Term_Query', and 'get_terms()'.
So, I suggest a new parameter 'parents__in' to get child terms from multiple parent terms IDs. The parameter on get_terms() will be like below:

<?php
    /**
     *
     *  @type int[] $parents__in 
     *  Array of comma-separated parent terms ID to retrieve child terms of given array.
     *  Default empty array.
     *
     */
    get_terms( array(
        'taxonomy'    => 'category',
        'parents__in' => array( 2, 3, 4 )
    ) );

Trac ticket: https://core.trac.wordpress.org/ticket/59503

This Pull Request is for code review only. Please keep all other discussion in the Trac ticket. Do not merge this Pull Request. See GitHub Pull Requests for Code Review in the Core Handbook for more details.