While the RAW say you can, it would be insane to allow it.
I once saw Arcane Thesis being manipulated to elevate a 1st level spell into an insane power.
The spell was eventually cast as a 9th level spell, but involving a total of 8 or more metamagic feats (don't remember the exact details), it became an auto-win spell.
It's insane if someone stacks metamagic onto the best spells, less so if they take a sub-par spell and boost that into the stratosphere. For instance, a
maximized empowered twinned repeated echoing [other stuff] summon monster IX can get you a lot of minions in a few rounds (like 22+2d4 bone devils) but isn't really going to break anything since they're nowhere near level-appropriate, and stacking a ton of metamagic to make an unreasonably-powerful
fireball just deals out an amount of damage comparable to an unreasonably-powerful martial character of similar level (240+20d6 damage from a
maximized empowered twinned energy-admixed [other stuff] fireball, vs. 10d6+290 from a 20th level fighter/barbarian/frenzied berserker with Power Attack, Leap Attack, Shock Trooper, and a
furious valorous speed weapon, and it can easily go higher) but more limited in times per day.
DMs should find out what a player wants to do with metamagic reducers before banning them out of hand, as in many cases Arcane Thesis is okay because the metamagics used with them are over-costed to begin with. The example
cone of cold is spending at least 3 feats to deal up to 15d6+10 cold damage plus slipperiness in one of several areas, more feats if he also wants to Silent and Still and such. If he were to instead spend those feats on Sculpt Spell, Empower Spell, and Arcane Thesis (Fireball), he could do 15d6 fire damage in one of several areas out of a 4th level slot. An extra 10 damage plus pseudo
grease is probably worth a +1 slot adjustment, and 3 feats had
better give you more bang for your buck than the 1 feat for an un-mitigated
empowered fireball, so in the grand scheme of things Arcane Thesis isn't all that bad in this instance.