Can I add internal search results to a 404 page in Shopify?

[KieranR]

Is it possible to include Shopify internal search results onto the 404 page? 

For example if someone tries to load 404 page: 

https://buystuff.com/products/green-bicycle-wheels?parameter=something&utm_source=xyz

Then I'd want to pull out the green-bicycle-wheels

and return search results for "green bicycle wheels" directly on the 404 page. 

So instead of just "404 page not found" I would like to attempt to provide some value in edge cases. 

We already feature "top products" and "you might also like" sections on our 404's but really looking to provide some more relevant stuff, does anyone know if this is doable within liquid?