It costs a bit, but the half-farspawn template in Lords of Madness grants 2 extra tenacles and more for a +4 LA.
Also if you want to go all out on the illithaid, there is the mind flayer, Ulitharid that is ECL 21 with 6 tenalces base. Both of these cost a boat load, but when going illithaid, what doesn't.
The question is do you just want tons of tenacles, or tons of tenalces on an illithiad? For the illithiad and assuming extreme cheese:
Psionic Mind Flayer 8 HD/7 LA/1 Thrallherd/1 Body Tamer/ 3 Illithiad Savant
Psionic version is in the expanded psions handbook and looses spell-likes for 9 levels of telepathy manifesting. Thrallherd will give you thralls as usual. Body tamer tenalce master. Illithiad savant is to focus on eating Legacy Champions from Weapons of Legacy. If you can get ahold of 1 level 10 legacy champion, you can eat his class ability to advance classes by 8 levels. Extended levels of the savant first to level 10 to get more eats. If you eat all 3 times (True Res as necessary on original champion), you can push your 3 PrC's to a total of 29 levels maxing all but one out. It is enough to get your manifestor progression to level 17 and two thralls.
If you cannot find a legacy champion, you could always thrallherd one with lesser effect.
Pushing this further, you could eat the SU ability alternative form for the pseudonatural creature (+12 LA, use a thrall to pick one up depending if you get to go off of your ECL or HD). This is iffy, but when in the pseudo form, all natural attacks become tentacle rake attacks + you get additional attacks based on HD. The reason this is iffy because the attack info is not listed under alternative form directly but under attack. If this worked though, you could get 4 additional attacks plus 1 for each other natural attack you picked up. With this trick active, you could always drop the body tamer and eat morphic weapons from warshaper that someone mentioned before. You have to be in a different form for this to work, but you can be as long as you like with alternative form. Note alternative form does not allow entry into warshaper, but it does not state the abilities fail to work when in an alternative form.
So without body tamer:
Psionic Mind Flayer 8 HD/7 LA/1 Thrallherd/4 Illithiad Savant
Two class eats for +16 levels to max Thrallherd and savant.
One class eat for Morphic weapons
1 SU eat for alternative form from pseodnatural creature
works well, but is not really too over the top with what you see typical savant do (or druid 20).