Is it possible to extend a class dynamically?

Yes. I like the answer with eval, but a lot of people afraid of any eval in their code, so here's one with no eval:

<?php //MyClass.php 
namespace my\namespace;
function get_dynamic_parent() {
    return 'any\other\namespace\ExtendedClass';// return what you need
}
class_alias(get_dynamic_parent(), 'my\namespace\DynamicParent');

class MyClass extends DynamicParent {}

While it's still not possible and not exactly your answer i needed the same thing and didn't wanted to use eval, monkey-patching etc. So i used a default class by extending it in conditions.

Of course it means if you have 100 classes to extend you need to add 100 conditions with another extending operation but for me this looked like the right way.

<?php
if(class_exists('SolutionClass')) {
    class DynamicParent extends SolutionClass {}
} else {
    class DynamicParent extends DefaultSolutionClass {}
}

class ProblemChild extends DynamicParent {}
?>