Opinion time please ...or rules too!
Extra mythic action (and possibly others) state that extra standard actions cannot be used to cast spells, would this apply to spell like abilities?
Can spell like abilities benefit from using metamagic rods?
Spell-like abilities are not spells. I'd say yes. Would you allow Extra mythic action to let you use a supernatural ability? Supernatural abilities are magical too.
The word cast is what is going to cause confusion. It was ruled in the past that being able to use a spell-like ability counts as being able to cast a spell. Does that mean that using spell-like ability is considered casting a spell? I anticipate many people will disagree on that.
The metamagic rod bit is a no, as metamagic feats cannot be applied to spell-like abilities. There are a few metamagic-like feats specifically for spell-like abilities, though.
Not sure about the extra standard action question.
Amazing Initiative (Ex): At 2nd tier, you gain a bonus on initiative checks equal to your mythic tier. In addition, as a free action on your turn, you can expend one use of mythic power to take an additional standard action during that turn. This additional standard action can't be used to cast a spell.
Spell-Like Abilities (Sp) Spell-like abilities are magical and work just like spells (though they are not spells and so have no verbal, somatic, focus, or material components).
Metamagic feats do not affect spell-like abilities.
Cool. Half of that was answered easily. I do believe that the answer for both should be no but thought that I'd get a poll for my players.