I think the best way of going about that, rather than setting up fixed-quantity, fixed-price multi-packs, would be to set it up as a single regular product with "Let buyer edit quantity" enabled.
This would allow you to select a Package Type unique to that product with a Packing Capacity of 1 (so each unit would be treated as being shipped in a separate parcel), and either specify an accurate shipping Weight for the product (including the weight of the container itself and any packing/padding materials) for UPS/USPS live rate lookups, or else specify a flat Cost for that Package Type (in Cart Shipping Settings) which would serve as a per-unit flat shipping fee for that item.
Then you can set up a series of product-specific automatic discounts that kick in when certain Min. Item Qty. thresholds are met for that item. Product-specific discounts alter the original per-unit price of the item, and if you leave the Discount Code field blank, each discount would be automatically applied in the buyer's cart when their order reaches the Min. Item Qty. threshold for that discount, and a discount with Min. Item Qty. = 10 would override one with Min. Item Qty. = 2 when that higher threshold is met.