Product Bundles and Groups of Products

[SoccerGuy3]

Looking at PrestaShop as a possible solution to a challenge I have with a new client's site. 

 

One:

I need the ability to take a group of products and put them together in a bundle. Customers will need to select from three categories of products. Each category in the group could have 2-9 items (not every item would need to be selected, but multiple items could be - think checkboxes I guess), each with color variations and possible upcharges. This entire package is then added to the cart under a single calculated price.

 

Two:

I need the ability to take a group of products and present to the customer. From there they can choose any of the products and set a quantity of each product they would like to order. However, they may not necessarily select ALL the products, just some of them. These would be added to the cart as individual items from a single "add to cart" button on the page.

 

Can Prestashop handle something like this?