air
bare
care
dare
err (depending on your pronunciation)
fare
glare
hare
lair
mare
ne’er
pare
rare
stair
tare
where
yare
Nope. Only 17.
Damn! Simulpost!
As a matter of fact, yes. 
bit
chit
dit
fit - flit
grit
hit
kit - knit
lit
mitt
nit
pit
quit
sit - slit - spit - split
tit
whit - wit - writ
zit
Only 16
-or also yields 16.
I forgot “whee” which makes 23 (19 if you thow out the ones that only represent the sounds of the letters)
blue - boo - brew
chew - clue - coo - crew - cue
dew - do - drew - due
ewe
few - flew - flu
glue - gnu - goo - grew
hew - hue
jew
knew
lieu
mew
new
pew
queue
rue
screw - shoe - skew - slew - spew - stew - sue
threw - through - thru - to - too - true - two
view
who - woo
yew - you
zoo
21, and that’s not counting the letter “u”. Woo Hoo!
You forgot “achoo”!
Edit I forgot about the mono-syllable rule.
Actually, that’s only 17 with the way the OP is counting (“brie” and “bee” count only as one, as they both start with “b.” Note the OP counts “funk” and “flunk” as one, as well as “sunk” and “stunk.”)
Nice going.
You can make it twenty two without stretching too much.