Based on http://www.wpexplorer.com/wordpress-page-templates-plugin/

page-templater.php

<?php

/**
 * Page Template main class
 */
class PageTemplater {

	/**
	 * A reference to an instance of this class.
	 */
	private static $instance;

	/**
	 * The array of templates that this plugin tracks.
	 */
	protected $templates;

	/**
	 * Returns an instance of this class.
	 */
	public static function get_instance() {

		if ( null === self::$instance ) {
			self::$instance = new PageTemplater();
		}

		return self::$instance;

	}

	/**
	 * Initializes the plugin by setting filters and administration functions.
	 */
	private function __construct() {

		$this->templates = array();

		// Add a filter to the attributes metabox to inject template into the cache.
		if ( version_compare( floatval( get_bloginfo( 'version' ) ), '4.7', '<' ) ) {

			// 4.6 and older.
			add_filter( 'page_attributes_dropdown_pages_args', array( $this, 'register_project_templates' ) );

		} else {

			// Add a filter to the wp 4.7 version attributes metabox.
			add_filter( 'theme_page_templates', array( $this, 'add_new_template' ) );

		}

		// Add a filter to the save post to inject out template into the page cache.
		add_filter( 'wp_insert_post_data', array( $this, 'register_project_templates' ) );

		/**
		 * Add a filter to the template include to determine if the page has our
		 * template assigned and return it's path.
		 */
		add_filter( 'template_include', array( $this, 'view_project_template' ) );

		// Add your templates to this array.
		$this->templates = array(
			'template-one.php'   => esc_html__( 'Template One', 'plugin-slug' ),
			'template-two.php'   => esc_html__( 'Template Two', 'plugin-slug' ),
			'template-three.php' => esc_html__( 'Template Three', 'plugin-slug' ),
		);

	}

	/**
	 * Adds our template to the page dropdown for v4.7+
	 *
	 * @param array $posts_templates Array of post templates.
	 * @return array $posts_templates Updated array of post templates.
	 */
	public function add_new_template( $posts_templates ) {
		$posts_templates = array_merge( $posts_templates, $this->templates );
		return $posts_templates;
	}

	/**
	 * Register post templates
	 *
	 * Adds our template to the pages cache in order to trick WordPress
	 * into thinking the template file exists where it doens't really exist.
	 *
	 * @param  array $atts Array of attributes.
	 * @since 1.0.0
	 */
	public function register_project_templates( $atts ) {

		// Create the key used for the themes cache.
		$cache_key = 'page_templates-' . md5( get_theme_root() . '/' . get_stylesheet() );

		// Retrieve the cache list.
		// If it doesn't exist, or it's empty prepare an array.
		$templates = wp_get_theme()->get_page_templates();
		if ( empty( $templates ) ) {
			$templates = array();
		}

		// New cache, therefore remove the old one.
		wp_cache_delete( $cache_key , 'themes' );

		// Now add our template to the list of templates by merging our templates
		// with the existing templates array from the cache.
		$templates = array_merge( $templates, $this->templates );

		// Add the modified cache to allow WordPress to pick it up for listing
		// available templates.
		wp_cache_add( $cache_key, $templates, 'themes', 1800 );

		return $atts;

	}

	/**
	 * Checks if the template is assigned to the page
	 *
	 * @param  string $template Template file.
	 * @return string $template Template file.
	 */
	public function view_project_template( $template ) {

		// Get global post.
		global $post;

		if ( is_singular( 'custom-post-type' ) && ! file_exists( get_stylesheet_directory() . '/single-custom-post-type.php' ) ) {
			$template = plugin_dir_path( __FILE__ ) . 'single-custom-post-type.php';
		}

		// Return template if post is empty.
		if ( ! $post ) {
			return $template;
		}

		// Return default template if we don't have a custom one defined.
		if ( ! isset( $this->templates[get_post_meta(
			$post->ID, '_wp_page_template', true
		)] ) ) {
			return $template;
		}

		$file = plugin_dir_path( __FILE__ ). get_post_meta(
			$post->ID, '_wp_page_template', true
		);

		// Just to be safe, we check if the file exist first.
		if ( file_exists( $file ) ) {
			return $file;
		} else {
			echo $file;
		}

		// Return template.
		return $template;

	}

}

add_action( 'plugins_loaded', array( 'PageTemplater', 'get_instance' ) );