Let's assume Conina the Barbarienne is the proud owner of a +5 anarchic furious courageous evil outsider bane greataxe (which, unless my math fails me, is a +10 equivalent)
Now, Conina comes to face a devil and flies into a battle rage.
Prize question: What is the weapon going to do? Applying the increase to effective enhancement granted by bane and furious would take the total effective enhancement quite a bit above +10...
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Pg 468 of the core rulebook, right below table 15-8 has your answer
"A single weapon cannot have a modified bonus (enhancment bonus plus special ability bonus equivalents, including from character abilities or spells) higher than +10."
Therefore your weapon would be +10 to hit and inflict 1d12+10 plus 4d6 damage plus whatever other non-enhancment bonuses from spells and feats and abilities you might have.
In regards to going over +5 things loke bane can go over this. A bane sword is one of the few ways to beat dr epic without a dm plot item. However I'm not sure where in the rules it says you can do this.
On the general question I'm not sure if stuff like bane or furious adjust the total. I think it stays a +10 weapon. But really yout in dm fiat territory.
*groan*
There is absolutely no impact from the +10 maximum enhancement. The rule William quoted is being obeyed - enhancement plus special ability equivalents total +10.
When the weapon gets stronger against individual monsters, that's the function of the special abilities. There is no rule against having higher than +5 enhancement in effect, just a restriction against crafting (or otherwise modifying) it to higher than +5.
So you'd have +9 enhancement bonus to attack and damage (and for courageous effects), and weapon damage increased by 2d6 from bane, as well as 2d6 chaotic damage added.
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Ok, I found a FAQ that covers this. I was partially wrong.
Weapon Bonuses: Can weapon special abilities (such as bane) or class abilities (such as a paladin's divine bond) allow you to exceed the +5 enhancement bonus limit and the +10 bonus-equivalent limitation?
For the enhancement bonus limitation, it depends on the specific effect or ability that's altering the weapon.
Bane: This allows the weapon to exceed the +5 limit, but only against the designated creature type. For example, a +5 dragon-bane longsword is normally a +5 weapon, but has a +7 enhancement bonus against dragons and deals +2d6 points of damage against dragons.
Paladin: The divine bond ability says "These [enhancement] bonuses can be added to the weapon, stacking with existing weapon bonuses to a maximum of +5." That means if a paladin has a +5 longsword, she can't use her divine bond to increate the enhancement bonus to +6 or higher (but she could use her bonuses to add abilities such as flaming to the weapon).
The +10 bonus-equivalent limitation is a hard cap for all weapons; you can't exceed that even with class abilities or other unusual abilities.
Bolded mine. You can't exceed the +10 cap EVER.