Can I add to an existing Entity schema from my own custom module
your my_module_schema_alter is missing a schema parameter.

fixed:

function my_module_schema_alter(&amp;$schema) {
  $schema = array();
  // Create the quiz node results table
  $schema['quiz_node_results']['fields']['time_taken'] = array(
    'type' =&gt; 'int',
    'size' =&gt; '10',
    'not null' =&gt; TRUE,
    'default' =&gt; 0,
    'description' =&gt; 'Stores the user inputted estimated time.',
  );
}