How can I add more “filters” to my products? (Categories, attributes, etc.)

I presume here that you’re using a shopping cart system such as WooCommerce?? If that’s the case, you could create new taxonomy terms for the products cut that WooCommerce creates using something like the below:

// Create custom taxonomy for parts CPT
add_action( 'init', 'create_vehmake_taxonomy' );
function create_vehmake_taxonomy() {
    register_taxonomy(
        'veh-make',
        'product', // CPT slug here
         array(
            'label' => __( 'Vehicle Make' ),
            'rewrite' => array( 'slug' => 'make' ), // Tax Term Slug (URL)
            'hierarchical' => true,
        )
    );
}

You could in theory create multiple of these to cater for your needs.

However, for ease of use, I’d probably be more inclined to use the Advanced Custom Fields plugin to create new meta fields on your product CPT that you can then use as select fields or text inputs to populate the data you need on a per-product basis.