Is it possible to have two seperate Carts on WooCommerce?

I’m trying to create a custom WooCommerce Cart. It would have the same capabilities as the real WooCommerce Cart. The only difference would be that in each cart, only specific types of products can go in.

Let’s say I have a session variable that tells me which products to show. And based on that session variable, I add products to a specific cart. And you can always change that session variable but keep the products for each cart until the session ends.

After that, I go to the checkout and it will list items from the specific cart based on that session variable once again.

Is something like that possible, specifically having two separate WooCommerce carts, the default one and a new custom one?

I tried this:

if (! isset(WC()->cart_custom) || '' === WC()->cart_custom) {
    WC()->cart_custom = new WC_Cart();
}

but every time I add products to the default cart and open the default cart page, the default cart is emptied. I don’t know why.

I hope my question makes some sense.