I don’t know what you’re using for the sax sound, but usually modulation does vibrato. If the sample has velocity layers, make good use of them 
…is go for a couple of sax lessons?
Exactly!
…or invite Wim (hornforhire) onboard 
He’s certainly my ‘secret to playing great sax’ 
Aloha guys,
To chime in…
As a MIDI guitarist my challenge when trying to sound like ANY
wind instrument is to remember to breathe.
Pianist and guitarist can play long lines of notes and do not
always have to think about taking a breath.
But horn players do and this fact helps to shape
the ‘nature’ of the solo.
(OTOH there is the 'circle breathing" technique
but it used mainly for effect and is not normally used in a ‘typical’ solo.)
My 2cents
{‘-’}
Same here! I’ve always said: I may suck, but I don’t blow!
The current record for continuous playing is 45 minutes and 47 seconds, held by saxophonist Kenny G 
It’s called ‘circular breathing’ and the first time I heard it was in a live recording by the Jazz Crusaders. Kenny G’s originally from this area, nice guy and while I don’t find his music particularly inspiring, I’d gig with him.
Yeah, live sax players ARE definitely better, but if you must use a sax VST to get your musical ideas across, I suggest:
The real secret is…
Get Wim to play it!
simples
That vid cracked me up. I stopped watching at the moment where he (presumably) forced all of the air from his lungs and then pronounced,
I don’t having any air in my lungs."
If he didn’t have any air in his lungs, then how was he able to say that at all?
I mean, what the hell?
I need to go back and watch the rest of the vid, but at that particular moment, he kinda destroyed his own credibility - in a ventriloquist-fail, “I-can-see-his-lips-moving!”’ kind of way. 
+1
Wim’s a fine player.
Velocity layers are usually accessed using the CC 11 (Expression) data.
No no…Velocity is not the same as Expression. The two frequently (but not always) go hand in hand, but you have to draw them separately.
Velocity is mapped directly to the first 8 data bytes of the MIDI Note On event. Expression is a controller, which is a separate MIDI message.
Velocity affects the volume (and typically only the volume). Expression is what you really want to use for VST versions of acoustic instruments (saxes, horns, etc.) to get the intended effect.
Be careful with pitch bends on saxophones. On the real instrument, a pitch bend (not including vibrato) affects the quality of the sound in addition to the pitch because they are accomplished by “opening” up the jaw. I have yet to hear a virtual sax that properly emulates this timbre change.
Sorry 'bout nitpicking, but: it’s 7 data bits. Definitely not 8 bytes.
The Data byte after the Status byte is always 7 bit info with the most significant bit 0 hence the 127 or 128 if you prefer.
I rest my case…
Could it be this!!!
Sue me. Yes, I mistyped the bits vs. bytes. And thank you for the correction on the 7 vs. 8. I was operating from memory.