canoeable
foie gras
But it wasn’t so qualified in the OP.
My OP. 
yeaed (as in “yeaed or nayed”) Example of use.
sauerkraut
Sioux.
Queue.
I had my dog dewormed and defleaed. Example of use
Tomorrow, I am defleaing my cat. Example of use.
Tennesseean
Now up to 63 of the 125 three-vowel combos with my latest bolded additions:
aaa
aae – baaed
aai – baaing
aao
aau
aea – panacaea
aee
aei
aeo – archaeology
aeu – Weyerhaeuser/ (forest products company)
aia – Praia (capital of the nation of Cape Verde)
aie – gaiety
aii – Hawaiian
aio – aioli
aiu
aoa – Quaoar (also works for uao)
aoe
aoi – Taoism
aoo
aou – miaouing
aua – Kauai
aue – sauerkraut
aui – Maui
auo
auu
eaa
eae – yeaed
eai – yeaing
eao
eau – beautiful
eea – Tennesseean
eee – créée (French word meaning created)
eei – seeing
eeo
eeu
eia – onomatopoeia
eie –
eii
eio
eiu
eoa – archaeoaeolotropic
eoe
eoi – geoids
eoo
eou – beauteous
eua
eue – queue
eui
euo – euouae
euu
iaa
iae
iai
iao – miaouing
iau
iea
iee
iei
ieo
ieu – lieu
iia – Hawaiian
iie
iii
iio
iiu
ioa – Ohioan
ioe – mustachioed
ioi
ioo
iou – curious
iua
iue – Niue (Pacific island)
iui
iuo
iuu
oaa
oae – archaeoaeolotropic
oai – moai
oao
oau
oea – canoeable
oee
oei – onomatopoeia
oeo
oeu – manoeuvre
oia – sequoia
oie – foie gras
oii
oio
oiu
ooa – wooable
ooe – shampooed
ooi – booing
ooo
oou
oua – euouae
oue – moue
oui – miaouing
ouo
ouu
uaa – Quaalude
uae – euouae
uai – quail
uao – Quaoar (Kuiper Belt object)
uau – luau
uea – squeal
uee – squeegee
uei – queueing
ueo – aqueous
ueu – queue
uia – huia
uie – quiet
uii
uio – obsequious
uiu
uoa
uoe
uoi – sequoia
uoo
uou – superfluous
uua
uue – Uuencode
uui
uuo
uuu
On my trip to Hawaii, I got leied as soon as I stepped off the plane!
No? How about this one:
My dog is Shar-peiesque.
Or maybe:
No, I.M. Pei didn’t design that building, but it is Peiesque.
Cite.
Well sure, you’re a Capricorn, but that was very Leoesque behavior.
I’m not a newbie, but I have a newbieish question.
Oh, hell, let’s knock out a few more. it will takes some (more) stretches:
Leaky’s office was littered with his Olduvaian finds.
It wasn’t a Kia, but it was Kiaesque, with many Kiaish design features.
That building has some Peiish design features.
I don’t know what was in that Hawaiian dish, but it had a poiish taste.
The island had a Rapa Nuiish atmosphere.