As per this FAQ being grappled doesn't prevent you from making a full attack so long as you are using one-handed or light weapons. Natural wepons are considered light.
So, In round 1 it would get 3 attacks and a free grapple attempt with each. If any of those grapple attempts are successful then on round 2 it would get 5 attacks. This is because of how rake works.
A creature with this special attack gains extra natural attacks under certain conditions, typically when it grapples its foe. In addition to the options available to all grapplers, a monster with the rake ability gains two free claw attacks that it can use only against a grappled foe. The bonus and damage caused by these attacks is included in the creature’s description. A monster with the rake ability must begin its turn already grappling to use its rake—it can’t begin a grapple and rake in the same turn.
Now, once it gains the grappled condition then under normal circumstances it would no longer threaten the squares around it. Grab lets it get around this, but only if it takes a -20 on it's subsequent grapple checks.
There are 2 scenarios that can arise from this.
Scenario A: Turn 1, the tiger focuses all of it's attacks on one enemy. Getting up to 3 grapple attempts. If one of them is successful then the both the tiger and it's target are grappled. Assuming the enemy was unable to break free, On Turn 2, the tiger makes a grapple attempt to maintain the grapple at a +9 bonus (+4 for grab and +5 because the enemy failed to break free). If it beats the target's CMD, It may now get 5 attacks on this enemy since it can make a full attack using it's two rake attacks.
Scenario B: Turn 1, the tiger attacks 3 different enemies in melee range. The free grapple attempts would be made at a -16 (+4 for grab and -20 for only using one limb). If it successfully grapples all 3 of them. Assuming none of the enemies are able to break free, On Turn 2, the tiger may choose 1 of the 3 creatures to hang on to, the other two are released. The tiger then makes a check at a -11 (+4 for grab, +5 because the enemy failed to break free, -20 to grapple with one limb). If the tiger is able to hang on to it's target. The target automatically takes damage for the limb used to maintain the grapple (claw or bite). The tiger can now make 2 additional attacks either at the target grappled or other enemies in range. As well as 2 rake attacks against the enemy that it held onto. Potentially it could use it's two attacks against the enemies it released and "re-grab" them. These checks would be at a -16 as before.
Kailas, ty, some small notes though:
For rake in first round:
Pounce (Ex)
FAQ
[Source]
When a creature with this special attack makes a charge, it can make a full attack (including rake attacks if the creature also has the rake ability).
Format: pounce; Location: Special Attacks.So tiger can pounce and rake in first round before grapple. But that is just a minor point, grapple is the issue :)
Basically all of the above can be done, with -20 on check to mantain grapple the following round (and no penalty except those from grappled condition while trying to initiate grapple while using normal attacks with grab in FIRST round against second and third target)?
Jeesh!
ah, yeah I forgot that pounce lets you make use of your rake attacks. You would still have to follow all the normal rules for charging, so it would depend heavily on positioning if there would even be more than 1 enemy to attack 5 times with the pounce. Since the rake gives you actual attacks pounce would make it so that the rake attacks can be used to initiate a grapple, via grab.
Maintaining a grapple is a standard action, the tiger cannot maintain the grapple and full attack in the same round. Best case is to maintain with the damage option for one bite worth of damage and then make the 2 free rake attacks.