How would you structure this?

I am designing a base that contains product info, but the spec has just changed and I need a bit of help understanding the best structure. For simplicity let’s assume I have a table of products and a linked table of factories.

ID Make Model Factory (linked)
100 Box Elite 2300 Belfast
101 Faithful Standard 20 Dublin
102 Universal 2020 Type 1 London

But now I’m being told that each product has multiple assembly’s, depending on a product type.

ID Make Model Type Factory (linked)
100 Box Elite 2300 Hand tool Belfast
101 Faithful Standard 20 Power tool Dublin
102 Universal 2020 Type 1 Inspection tool London
and each type will have multiple assemblies which may be manufactured in different factories.

So do I need to have multiple rows in my product table?

ID Make Model Type Assembly Factory (linked)
100-A Box Elite 2300 Hand tool Blade Belfast
101-B Box Elite 2300 Hand tool Plastics Newtown
101-C Box Elite 2300 Hand tool Packaging Dublin

or can I somehow structure the base to create a link between product and type and the assembly that then links to a particular factory?

Since we have to search for products I’m not keen to have multiple rows per product (as in the live base there are likely to be up to 12 assemblies per product).