The Soulknife subclass of rogue has the "psychic blades" ability, which says this:
You can manifest your psionic power as shimmering blades of psychic energy. Whenever you take the Attack action, you can manifest a psychic blade from your free hand and make the attack with that blade. This magic blade is a simple melee weapon with the finesse and thrown properties. It has a normal range of 60 feet and no long range, and on a hit, it deals psychic damage equal to 1d6 plus the ability modifier you used for the attack roll. The blade vanishes immediately after it hits or misses its target, and it leaves no mark on its target if it deals damage.
After you attack with the blade, you can make a melee or ranged weapon attack with a second psychic blade as a bonus action on the same turn, provided your other hand is free to create it. The damage die of this bonus attack is 1d4, instead of 1d6.
Why is this ability entirely incompatible with extra-attack? For instance, if I multi-classed into fighter, taking five levels, why can I not make a psychic blade for both my attacks? Why do I have to use a bonus action to make another one? Does it make sense to just say I can make another one with my second attack but it only does 1d4?
It's perfectly compatible with Extra Attack. You just can't use it in your extra attacks. You have to use another weapon but your Extra Attack feature works just fine. Plus, you get a pseudo light weapon attack as a Bonus Action.
The rest of your question is a house rule question because attacking with it multiple times in the attack action is not RAW.
Why did the designers make this design choice? Probably to restrict the follow up abilities relating to attacking with your psychic blades.
Oh, also, one more thing if it helps somehow. The feature has been updated in the 2024 PHB. Now it can be used with Opportunity Attacks.
Level 3: Psychic Blades
You can manifest shimmering blades of psychic energy. Whenever you take the Attack action or make an Opportunity Attack, you can manifest a Psychic Blade in your free hand and make the attack with that blade. The magic blade has the following traits: [...] The blade vanishes immediately after it hits or misses its target, and it leaves no mark if it deals damage.
After you attack with the blade on your turn, you can make a melee or ranged attack with a second psychic blade as a Bonus Action on the same turn if your other hand is free to create it. The damage die of this bonus attack is 1d4 instead of 1d6.
I really don't see a problem between Extra Attack feature and Psychic Blades.
Attack Action:
When you take the Attack action, you can make one attack roll with a weapon or an Unarmed Strike.
Level 5: Extra Attack
You can attack twice instead of once whenever you take the Attack action on your turn.
It should just let you attack twice with the main blade (or repeat twice the attack if you will). Since psychic blades is not a replacement effect of the attack action or is it considered that?
To each his ownI guess, and talk to your DM about it.
I really don't see a problem between Extra Attack feature and Psychic Blades.
The psychic blades disappear after they are used to attack so they can't be used as the only weapon to attack multiple times as part of the attack action. They can be used as one of the weapons just fine.
The Soulknife subclass of rogue has the "psychic blades" ability, which says this:
You can manifest your psionic power as shimmering blades of psychic energy. Whenever you take the Attack action, you can manifest a psychic blade from your free hand and make the attack with that blade. This magic blade is a simple melee weapon with the finesse and thrown properties. It has a normal range of 60 feet and no long range, and on a hit, it deals psychic damage equal to 1d6 plus the ability modifier you used for the attack roll. The blade vanishes immediately after it hits or misses its target, and it leaves no mark on its target if it deals damage.
After you attack with the blade, you can make a melee or ranged weapon attack with a second psychic blade as a bonus action on the same turn, provided your other hand is free to create it. The damage die of this bonus attack is 1d4, instead of 1d6.
Why is this ability entirely incompatible with extra-attack? For instance, if I multi-classed into fighter, taking five levels, why can I not make a psychic blade for both my attacks? Why do I have to use a bonus action to make another one? Does it make sense to just say I can make another one with my second attack but it only does 1d4?
It's perfectly compatible with Extra Attack. You just can't use it in your extra attacks. You have to use another weapon but your Extra Attack feature works just fine. Plus, you get a pseudo light weapon attack as a Bonus Action.
The rest of your question is a house rule question because attacking with it multiple times in the attack action is not RAW.
Why did the designers make this design choice? Probably to restrict the follow up abilities relating to attacking with your psychic blades.
How to add Tooltips.
My houserulings.
I also think it's right, but as discussed in Rogue/Ranger multiclass: How to use Ranger fighting styles with Soul Blades, just note that it doesn't work for dual-wielding light weapons, since it isn't a weapon with the Light property.
Oh, also, one more thing if it helps somehow. The feature has been updated in the 2024 PHB. Now it can be used with Opportunity Attacks.
Okay, do you think it is reasonable to allow it to work with extra-attack?
Sure! It's legit per the rules as SmiteMakesRight_3_5 said. Maybe you need to draw a weapon before the extra attack, but I'd say that's all.
EDIT: sorry, I didn't read the question properly. If your question is about attacking twice or more with the same Psychic Blade, that's DM territory.
But if it's fun for you and allowed by your DM, go for it :)
Give people multiple melee and or ranged attacks and they are still not happy.
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I really don't see a problem between Extra Attack feature and Psychic Blades.
Attack Action:
When you take the Attack action, you can make one attack roll with a weapon or an Unarmed Strike.
Level 5: Extra Attack
You can attack twice instead of once whenever you take the Attack action on your turn.
It should just let you attack twice with the main blade (or repeat twice the attack if you will). Since psychic blades is not a replacement effect of the attack action or is it considered that?
To each his ownI guess, and talk to your DM about it.
The psychic blades disappear after they are used to attack so they can't be used as the only weapon to attack multiple times as part of the attack action. They can be used as one of the weapons just fine.
How to add Tooltips.
My houserulings.