As others have mentioned there is the limit based on Charisma (Core book p. 235). Of course, that might not be a problem, if he has sufficient Charisma and doesn't use the Sprites too much.
One thing to remember, though, which applies to both Spirits and Sprites are that they aren't just semi-intelligent tools. They are semi-autonomous, entirely intelligent creatures. Both of which dislike being bound/registered. You could take a bit of time to sit down, and figure out exactly what personalities these guys have. Weird and alien digital intelligences.
The notes in the "Bound Spirits" box on p. 178 can be applied to Sprites as well, including the dice pool modifier. And do abuse the heck out of the information in the "Uncontrolled Sprites" box on p. 236, if he fails to re-register a sprite. If the sprites never become uncontrolled, then maybe there are free sprites that can bother the technomancer. All assuming of course that the technomancer is actually abusing the sprites.
Below are a couple of the sprites that the technomancer in my previous campaign had under her control.
Hex, Rating 4 Code Sprite
Tasks owed: 3
Pilot: 4
Response: 4
Firewall: 6
Matrix INIT: 8
IP: 3
EDGE: 4
RES: 4
Skills: Computer, Data Search, Electronic Warfare
Complex Forms: Analyze, Browse, Decrypt, Edit, Encrypt
Powers: Info Sortilege, Probability Distribution
Hex has little personality, and seem at its happiness when sitting in an
info-node sorting and collating data. When you are not calling upon its
services, it is doing just that. Luckily you can tell it to sit in places
where it is unlikely to be discovered, as long as there is enough information
flowing through. If there isn't, it may wander off, getting into nodes where it
draws unwanted attention from the defenses. These days it hangs out at the main
Seattle library, just browsing data all day long.
When revealed it looks like a small, gently swirling tornado of green code
strings.
Pulse, Rating 4 Data Sprite
Tasks owed: 4
Pilot: 4
Response: 4
Firewall: 2
Matrix INIT: 8
IP: 3
EDGE: 4
RES: 4
Skills: Computer, Data Search, Electronic Warfare
Complex Forms: Browse, Decrypt, Edit, Encrypt
Powers: Stenography, Watermark
You often get the feeling that Pulse is just doing with you as a side thing,
and is out doing things on a much grander scale when it isn't with you. Pulse
is serious, and can occasionally seem downright condescending when pointing out
a flaw in a plan of action. You can never help but feel that you are greatly
under appreciating its true potential.
When revealed it looks like a black irregular rectangle with a neon-green
border on a surface of the VR landscape. When moving, it moves along the
surface, though if there is no suitable surface to glide along, it will
occasionally take to the air, where it is still perfectly 2-dimensional.
Doc, Rating 4 Machine Sprite
Tasks owed: 4
Pilot: 4
Response: 4
Firewall: 6
Matrix INIT: 8
IP: 3
EDGE: 4
RES: 4
Skills: Computer, Electronic Warfare, Hardware
Complex Forms: Command, Medic
Powers: Diagnostics, Gremlins, Stability
Like Hex, Doc is a simple sort. Doc's passion seems to be keeping the datascape
in tip top form, whether organizing the icons, keeping a commlink working while
under cyber attack, or repairing damaged programs. It seems mindless as it
flutters from one job to the next, though it responds to commands. Doc is
different from the others, as in you didn't attract its attention by compiling
it. Instead you simply found it one day puttering around in the home network of
your parent's apartment.
Jaguar, Rating 4 Machine Sprite
Tasks owed: 4
Pilot: 4
Response: 4
Firewall: 6
Matrix INIT: 8
IP: 3
EDGE: 4
RES: 4
Skills: Computer, Electronic Warfare, Hardware
Complex Forms: Autosoft(Defense), Command
Powers: Diagnostics, Gremlins, Stability
Jaguar loves drones. He loves being in them, and especially seems to like your
Steel Lynxes. When he is in them, they act visibly more animal-like. In the
matrix, when not commanding a drone, he acts jittery, as if he would rather get
moving to some place else. And for some reason you get the distinct impression
that he is a he, and not a non-gendered it.
In the matrix he takes the form of a mechanical spider. Steel girder skeleton
overlain with wires arranged so that they resemble muscles. About a meter in
diameter and waist-high. Though he usually stays outside of the VR landscape,
he is less shy than Hex or Pulse about coming out into the open.