You said you weren't asking for a list, but I think making a list is the easiest way to answer this question. Filtering part-of-speech.txt, I found the following entries which matched A
, [Vti]
, N
, and v
simultaneously:
Ojibway Adjective, Adverb, Verb (transitive), Noun
ad-lib Verb (usu participle), Adjective, Adverb, Noun
aggregate Adjective, Noun, Verb (usu participle), Verb (transitive), Adverb
air-mail Adjective, Noun, Adverb, Verb (transitive)
back Noun, Adjective, Adverb, Verb (usu participle)
backhand Noun, Adverb, Verb (transitive), Verb (usu participle), Adjective
bad Adjective, Noun, Adverb, Verb (usu participle)
best Adjective, Adverb, Noun, Verb (transitive), Verb (usu participle)
better Adjective, Adverb, Noun, Verb (usu participle), Verb (transitive)
bias Noun, Adjective, Adverb, Verb (usu participle), Verb (transitive)
bitter Adjective, Adverb, Noun, Verb (usu participle)
blind Adjective, Adverb, Verb (usu participle), Verb (intransitive), Noun
blindfold Verb (transitive), Noun, Adjective, Adverb, Verb (usu participle)
broadcast Verb (usu participle), Verb (intransitive), Verb (transitive), Noun, Adjective, Adverb
broadside Noun, Adverb, Verb (usu participle), Adjective
champion Noun, Adjective, Adverb, Verb (transitive), Verb (usu participle)
clean Adjective, Verb (usu participle), Verb (transitive), Adverb, Noun
clear Adjective, Verb (transitive), Verb (intransitive), Adverb, Noun, Verb (usu participle)
close Verb (usu participle), Verb (transitive), Verb (intransitive), Adjective, Adverb, Noun
closer Noun, Verb (usu participle), Adjective, Adverb
cod Noun, Verb (usu participle), Adjective, Adverb
collect Verb (usu participle), Verb (transitive), Verb (intransitive), Adverb, Adjective, Noun
cool Adjective, Adverb, Noun, Verb (usu participle)
counter Noun, Adverb, Adjective, Verb (usu participle), Verb (transitive)
crescendo Noun, Adjective, Adverb, Verb (intransitive), Verb (usu participle)
crisscross Verb (usu participle), Adjective, Noun, Adverb
dam Noun, Verb (usu participle), Interjection, Adverb, Adjective
damn Interjection, Adjective, Adverb, Noun, Verb (usu participle)
darn Verb (usu participle), Noun, Interjection, Adjective, Adverb
dash Verb (usu participle), Verb (intransitive), Noun, Interjection, Adjective, Adverb
double Adjective, Noun, Verb (intransitive), Adverb, Verb (usu participle), Verb (transitive)
down Plural, Adverb, Verb (transitive), Verb (intransitive), Noun, Verb (usu participle), Adjective
dry Adjective, Verb (usu participle), Verb (transitive), Noun, Adverb
dryer Noun, Verb (usu participle), Verb (transitive), Adjective, Adverb
even Adjective, Adverb, Noun, Verb (usu participle)
express Verb (transitive), Adjective, Noun, Adverb, Verb (usu participle)
fair Adjective, Adverb, Verb (intransitive), Noun, Verb (usu participle)
fast Adjective, Adverb, Interjection, Verb (intransitive), Noun, Verb (usu participle)
fine Noun, Verb (transitive), Verb (usu participle), Adjective, Adverb
firm Adjective, Adverb, Verb (usu participle), Verb (intransitive), Noun
flat Adjective, Adverb, Noun, Verb (usu participle), Verb (intransitive)
flush Verb (usu participle), Verb (transitive), Noun, Adjective, Adverb
forehand Adjective, Noun, Adverb, Verb (usu participle)
forward Adjective, Noun, Adverb, Verb (transitive), Verb (usu participle)
foul Adjective, Noun, Verb (usu participle), Verb (transitive), Verb (intransitive), Adverb
free Adjective, Adverb, Verb (usu participle), Verb (transitive), Noun
freelance Noun, Verb (usu participle), Adverb, Adjective
fresh Adjective, Noun, Verb (usu participle), Adverb
fucking Adjective, Adverb, Interjection, Verb (intransitive), Noun
full Adjective, Adverb, Noun, Verb (transitive), Verb (intransitive), Verb (usu participle)
goldurn Noun, Adjective, Adverb, Verb (transitive)
grave Noun, Adjective, Verb (usu participle), Verb (transitive), Adverb
home Noun, Adjective, Adverb, Verb (intransitive), Verb (usu participle)
hugger-mugger Noun, Adjective, Verb (transitive), Verb (intransitive), Adverb
huggermugger Noun, Adjective, Adverb, Verb (usu participle), Verb (transitive), Verb (intransitive)
hurry-scurry Noun, Adverb, Adjective, Verb (intransitive)
hurry-skurry Noun, Adverb, Adjective, Verb (intransitive)
jolly Adjective, Adverb, Verb (transitive), Noun, Verb (usu participle)
last Adjective, Adverb, Noun, Verb (usu participle), Verb (transitive)
left Adjective, Adverb, Noun, Verb (usu participle)
licht Noun, Adjective, Verb (transitive), Verb (intransitive), Adverb
light Noun, Adjective, Verb (usu participle), Adverb, Verb (intransitive)
like Adjective, Plural, Adverb, Conjunction, Noun, Verb (transitive), Verb (usu participle)
long Adjective, Noun, Adverb, Verb (intransitive), Verb (usu participle)
loose Adjective, Noun, Adverb, Verb (transitive), Verb (usu participle)
low Adjective, Adverb, Noun, Verb (usu participle)
near Plural, Adverb, Verb (usu participle), Noun, Adjective
ok Noun, Verb (usu participle), Adjective, Adverb
okay Adjective, Adverb, Verb (transitive), Noun, Verb (usu participle)
out Adverb, Plural, Interjection, Noun, Verb (transitive), Verb (intransitive), Verb (usu participle), Adjective
part Noun, Adverb, Verb (usu participle), Verb (intransitive), Verb (transitive), Adjective
pat Verb (usu participle), Verb (transitive), Verb (intransitive), Noun, Adverb, Adjective
plain Adjective, Noun, Adverb, Verb (usu participle)
plumb Noun, Adjective, Adverb, Verb (usu participle)
plump Adjective, Verb (usu participle), Verb (intransitive), Noun, Adverb
pop Verb (usu participle), Verb (intransitive), Verb (transitive), Noun, Adverb, Interjection, Adjective
post Noun, Verb (transitive), Verb (intransitive), Adverb, Verb (usu participle), Adjective
prompt Adjective, Adverb, Verb (transitive), Noun, Verb (usu participle)
quiet Adjective, Noun, Verb (usu participle), Adverb
retail Noun, Adjective, Adverb, Verb (usu participle), Verb (transitive)
right Adjective, Adverb, Noun, Verb (usu participle), Interjection
rough Adjective, Noun, Adverb, Verb (transitive), Verb (usu participle)
round Adjective, Noun, Plural, Adverb, Verb (usu participle), Verb (transitive)
second Adjective, Noun, Verb (transitive), Adverb, Verb (usu participle)
sharp Adjective, Adverb, Noun, Verb (transitive)
sheer Adjective, Adverb, Noun, Verb (usu participle), Verb (intransitive)
shilly-shally Verb (intransitive), Noun, Adjective, Adverb
shillyshally Verb (usu participle), Adverb, Adjective, Noun
short Adjective, Adverb, Noun, Verb (usu participle)
slack Adjective, Adverb, Noun, Verb (usu participle)
smart Adjective, Verb (usu participle), Noun, Adverb
smooth Adjective, Adverb, Verb (usu participle), Noun
solo Noun, Adjective, Adverb, Verb (intransitive), Verb (usu participle)
sound Noun, Verb (usu participle), Verb (intransitive), Verb (transitive), Adjective, Adverb
square Noun, Adjective, Verb (usu participle), Adverb
steady Adjective, Verb (usu participle), Adverb, Noun, Interjection
still Adjective, Adverb, Noun, Verb (usu participle), Verb (transitive)
stone Noun, Adverb, Verb (usu participle), Verb (transitive), Adjective
subject Noun, Adjective, Adverb, Verb (usu participle), Verb (transitive)
summer Noun, Adverb, Verb (intransitive), Verb (transitive), Verb (usu participle), Adjective
thwart Verb (usu participle), Noun, Adjective, Plural, Adverb
tiptoe Verb (usu participle), Noun, Adverb, Adjective
traverse Verb (usu participle), Adverb, Verb (transitive), Verb (intransitive), Noun, Adjective
trim Adverb, Verb (transitive), Noun, Adjective, Verb (usu participle)
true Adjective, Verb (transitive), Noun, Verb (usu participle), Adverb
up Noun, Verb (usu participle), Adverb, Plural, Adjective
upgrade Verb (usu participle), Verb (transitive), Noun, Adjective, Adverb
upright Adjective, Adverb, Noun, Verb (transitive)
upstage Adverb, Adjective, Verb (transitive), Noun, Verb (usu participle)
war Adverb, Verb (usu participle), Noun, Adjective
well Adverb, Adjective, Interjection, Noun, Verb (usu participle)
wholesale Noun, Adjective, Adverb, Verb (usu participle)
worst Adjective, Adverb, Noun, Verb (transitive), Verb (usu participle)
wrong Adjective, Noun, Adverb, Verb (transitive), Verb (usu participle)
zigzag Noun, Adjective, Adverb, Verb (transitive), Verb (intransitive), Verb (usu participle)
You can judge for yourself the quality of the data. It might not be perfect, and you could argue that some of the entries don't really belong in this answer. However, I'm not going to edit it by hand; I think it's sufficient to see that the answer is Yes, there are other such words.
Still, if I want this answer to be complete, I think I need to pick a word from the list and demonstrate that it actually fits the pattern. The most obvious one to my eye is damn:
Adjective: "Argh! I hit my damn thumb again!"
Adverb: "He was running damn fast."
Verb: "And for his sins, he was damned to Hell."
Noun: "I don't give a damn."
There are other swears which are rather flexible in terms of parts of speech; I'll leave the list as an exercise to the reader.