Rarely more than three or four.
I'm not keen on high street shopping (although DH loves it and never shops online), but I don't really need much stuff. On the rare occasion I need clothing/footwear I'll buy that in a bricks and mortar shop as I hate having to do online returns if something doesn't fit etc.
So, online shopping is usually either books (but I do prefer a browse in Waterstones, for example, it's just they are invariably more expensive and I like to try to buy preloved where possible) or stuff for the home.
I tend to avoid Amazon but love ebay - many of our pieces of furniture and larger interior items are from eBay - but this week my one parcel is coming from an independent shop with an online presence. It's on the other side of the UK so too far to visit in person.
I agree it's more about the cost than the number of parcels though - ie, one week I might buy four (preloved) books from different sellers so arriving in four separate parcels , costing a total of £20. Whereas this week I've bought a bed throw (new) - so one parcel - costing £94.
DH did think I could find the latter locally, but having been dragged round the shops to no avail over the Easter weekend, he gave up and concurred that buying online was best in this instance!