From the thread "Augmented maximums and drugs"
QUOTE (Patrick Goodman @ Aug 9 2013, 09:12 AM)

...I can only speak to authorial intent, but this mirrors discussions with other writers in the development stage.
"First: if I already have my attribute at it's augmented maximum, does a drug have any effect, or is that the limit of that race's physiology? I.e. does a human with a modified strength of 10 become effective strength 12 when he is on kamikaze? I guess some clarity around "Augmentation" vs. "Effect" would be useful."
Yep. The drugs were meant to be scary in their effects, and were meant to be able to (temporarily, at some sort of cost) make you into a monster. So yeah, your modified human would be sporting a 12 STR while on the drug. At least that's what I had in mind.
So, from that reading I'd say there are specific circumstances where your attributes can (temporarily) exceed the augmented maximum. However, from re-reading "Push the limit", I'm not sure. I read "This use of Edge also allows you to ignore any limit on your test." as referring to limits related to dice pools (i.e. Mental, Physical, etc.) rather than the "limits" of your total attribute.
Attribute Boost reads:
"Each hit on this test boosts your attribute rating by 1,
up to your augmented Attribute maximum[emphasis mine]. This only affects your dice pools; your Physical limit and Initiative ratings don’t change with Attribute Boost. The boost lasts for a number of Combat Turns equal to twice the number of hits you get. When the boost runs out, you take Drain equal to the level of this power."
As a GM, I would rule that you could boost your attribute up to your augmented maximum using that power and no higher. HOWEVER, I would also rule it lasted a number of combat turns equal to twice the total number of ALL the hits you got- including the ones gained through the rule of 6 using edge. So, you can only have so high a strength or agility, but you can have it a LONG time.