Currently owned? The Alan Parsons Project.
Artist that I purchased the most of? Iron Maiden.
Ookla the Mok
I think I have everything by The Pogues. At least, I have most everything by them.
When I was ripping CDs a couple of years ago I was surprised to find it was Van Morrison.
Several artists in the low double digits. None more than 20. Beatles, Genesis, Old 97s, Rush, Richard Thompson, Wilco.
Ironically, I only own one Joe Jackson album. 
Wild for me too. I don’t mean to threadshit, but thought people might like a diversity of responses. I don’t own any vinyl anymore. When I did, probably 40 to 50 tops, with no more than 2 or maybe 3 of any particular artist. I might still own some CDs, but probably never owned more than 35-40 in my life.
The Kinks - 24 official releases, including imports, live LPs and greatest hits packages. Plus I don’t know how many cassette bootlegs. Plus several of Ray and Dave’s solo projects.
I think The Beatles and Green Day, with 14 each, are the only other artists that get into double digits.
Percentage-wise, I don’t think I have 100% from anyone that had more than one release. I thought maybe Traveling Wilburys, as I have both of their albums, but it turns out there was a later box set that included bonus tracks.
Well. I’m a piker next to some of y’all, but I think my answer is somewhat unique: Ani DiFranco. I have eight. Ten, if you count having to buy Living In Clip three times, because I kept losing it. Likewise, I’ve owned four copies of the Cowboy Junkies Trinity Sessions, three of Joan Osborne’s Relish, and three of Suzanne Vega’s Greatest Hits. I’m not the most organized of people…
digs, what’s wrong with Poco? Rose of Cimmaron is one of my go-to jams.
Yep. That’s me.
I just looked. I guess I have around 70 CDs. I know I’ve lost or lent out some over the years, so maybe 80, tops.
Peter Hammill, both solo, in collaboration or with VDGG. Something over 100 cds, plus official and bootleg vinyl & cassettes and the odd VHS or dvd. And a bunch of stuff by other VDGG members, etc…
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I spent quite a few years working at a record store, so my collection of LPs is in the thousands. At the end of every week the boss would go through the records we had been playing in the store and rotate out a selection of the older ones. These were divvyed up by the staff for our personal use.
Of course, there are a large number of albums that never even got played in-store - they went straight into somebodies collection. Jiggle pop anybody? I have that on vinyl. Don’t ask me why.
No contest.
Midnight Oil
Rush and Jimi. Got a lot of Stones, too.
Nothing, in fact I still think that Rose of Cimmaron and Bad Weather * are classic songs. And though I love their heyday with Richie Furey and Paul Cotton, they’re still recording, because Rusty Young is a great musician.
*It’s just so damn poignant and classy… here’s a performance that Richie and an accordion dropped in on.
BUT… my kids give me so much crap for it. That all started when they discovered the Ramones and I said “Damn, you guys are hipper now than I was then.” “Wait, what were you listening to then?” I could tell they wanted to scoff, so I shuffled guiltily and mumbled “Ummm, poco…”
I figured you probably have a good sized pile of DBT as well… 
Pink Floyd. In various formats, I have 7 copies of DSOM, and several copies of many others, but I’m just counting one-for-one here.
Jimi. Alan Parsons Project. Fleetwood Mac. Heart. John Cougar (Mellencamp). Police. Pretenders. Van Halen. George Carlin. Melissa Etheredge.
“Stay the blazes home” - Stephen McNeil, Premier of Nova Scotia
Warren Zevon. I have all of them, plus any collections, greatest hits, tributes, etc.
Most of the artists I like were either not that prolific, or had a lot of filler on their albums so a 'greatest hits collection is fine. For example, I’ll bet a LOT of Eagles fans only own their two greatest hits albums plus maybe ‘Hotel California’.
Oh, yeah, almost everything ever done by Joe Walsh, and quite a lot of Eno, including one of his iOS apps.