Replace Magento autoloader with composer based autoloader. Note: you are losing the ability to use the compiler.

app--code--local--Varien--Autoload.php

<?php
/**
 * Classes source autoload
 */
class Varien_Autoload
{
    /** @var \Composer\Autoload\ClassLoader */
    private static $autoloader;

    /** @var self */
    private static $instance;

    /**
     * Singleton pattern implementation
     *
     * @return Varien_Autoload
     */
    static public function instance()
    {
        if (!self::$instance) {
            self::$instance = new Varien_Autoload();
        }
        return self::$instance;
    }

    /**
     * Register composer autoloader
     */
    static public function register()
    {
        if (!static::$autoloader) {
            static::$autoloader = require __DIR__ . '/../../../../vendor/autoload.php';
        }
    }

    /**
     * Load class source code
     *
     * @param string $class
     * @return bool
     */
    public function autoload($class)
    {
        return static::$autoloader->loadClass($class);
    }

    public function registerScope($scope)
    {}

    public static function getScope()
    {}
}