Free shipping by number of items, not monetary value, in Bigcommerce - templates

Question

I've been asked by a client to look into the possibility of allowing free shipping for orders of more than three items. Essentially this means allowing for a (shipping) pricing structure based on item count rather than total value.
(For a TL;DR, you could probably stop with that problem statement, but I'll provide some solution investigation context below. Maybe I've missed something.)
The admin UI only allows for setting free shipping based on monetary value. Similarly, the "Ship by" category of price options adds the ability to use weight in calculations, but alas not item count.
There seems to be no way to influence the shipping cost through the API. A %%GLOBAL_ShippingPrice%% variable is available to templates and, as I understand things, is calculated only using those admin-configured shipping configuration options described above. The Shipping API only seems to deal with shipping methods (physical not API methods!), and unfortunately the Orders API seems to offer nothing related to shipping costs either. Hmm.
I've looked into hacking the template files, but cannot find any support for custom expressions using the variables available.
We've asked Bigcommerce support, submitted an "idea", and obviously searched the interwebs and poked around the developer documentation. I'm so new, I only heard about Bigcommerce yesterday.
Any suggestions will be greatly appreciated.
Note: First draft of this question included an inline screenshot and lots of relevant hyperlinks. Seems important for a quality question. Apparently I need more karma to insert most of that. I'll edit this question later, if possible and I ever get there, to include those helpful features.

Answer 1

Since Bigcommerce is not an open source platform, you cannot adjust things like shipping services and their actual functionality.
The only workaround I can think of would be to set every product to the same weight(1lb, for example) then set up shipping by weight which says cart >= 3lbs ships free. This will present a problem if you are using real time quotes from providers such as FedEx, USPS, or UPS though.
In the future I would suggest looking at their community forum(forum.bigcommerce.com) for questions such as this, since it does not actually pertain do the development of their API or templating system.
Best of luck!

Answer 2

This is possible if you use ShipperHQ. Here are the steps to configure it:
In ShipperHQ, ensure you have your UPS Carrier set with UPS Ground as
an available shipping method.
Click on Filters on the navbar and add
a new filter.
On your new filter, select “Whole Cart” under Filter
Applies To in the Edit Filter panel and enter a Name you’ll recognize
(e.g. “Over 3 items”).
In the Standard Filters panel, select “Range”
for the Quantity filter, enter a Min value of 3 and check the No Max
checkbox and Save.
You now have a filter set up which will match
against an order total with more than 3 items.
Click on Carrier
Rules on the navbar and add a new Rule.
Enter a descriptive Name
(e.g. “Free UPS Ground over 3 items”) under the Overview panel and
select UPS Ground in the Live Shipping Methods Assigned field under
the Applicable Shipping Methods panel.
In the Conditions panel,
select the Filter you just set up under Weight/Price/Quantity Filters
In the Actions panel and the Rule Action section, choose
“Set/Surcharge Shipping Methods” from the Action to Perform
drop-down, “Set Rates” from the Adapt Shipping Rates drop-down, and
“Per Cart” in the Apply Shipping Rate/Percentage drop-down.
In the
Set/Modify Shipping Rate section of the Actions panel, enter 0 in the
Shipping Rate field.
Save your rule.
ShipperHQ will now set UPS Ground to Free if the order has over 3 items.
Source: http://docs.shipperhq.com/how-to-set-up-free-shipping-for-orders-with-more-than-x-amount-of-items/