No, that would not make sense, but you can start with a Wizard, Sorcerer, or Warlock, and create a subclass that give spell blade abilities and surprise, and make a mage with assassin that has stealth bonuses attached to the use of certain magics etc.
A Sorcerer that can use their Sorcery points, when they have advantage, to add sneak attack damage as force (or whatever energy theme you chose with more sorcery points etc.) to certain weapon attacks...obviously they would be limited, due not being able to use them every round endlessly like a rogue, and you have a limited amount to use, but it gives the flavor. This would make it not OP too, because you will really need to think, do I use 4 points for this, or save some for twin spell? Since this becomes a super point use build, if you kill something with this skill, you get the points back. anyhow there are lots of possibilities to make this work and not be OP.
Basically you need to start your subclass within a full magic user...then make the subclass give rogue like perks that are tied to mage abilities. Remember, casters are already powerful, so you can not give the full ability that a rogue has, or they will be WAY to OP...and their rouge damage or abilities, can not out do rogues...for balance, and the fact mages already are awesome.
EDIT: What I do is take levels of Arcane Trickster, until I get the amount of sneak attack die I want, then just do the rest of the levels Wizard...makes for a super powerful Rogue/Mage.
I usually only do 2 levels of Wiz on an Arcane Trickster. It doubles the Arcane part of the character while still maximizing the Rogue aspect. With green-flame blade, that’s a lot of damage on a hit, and with something like Divination or Bladesinger as the Wiz subclass it really works well, even with only the 2 levels.
Is it possible to homebrew a full caster rouge?
No
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No, that would not make sense, but you can start with a Wizard, Sorcerer, or Warlock, and create a subclass that give spell blade abilities and surprise, and make a mage with assassin that has stealth bonuses attached to the use of certain magics etc.
A Sorcerer that can use their Sorcery points, when they have advantage, to add sneak attack damage as force (or whatever energy theme you chose with more sorcery points etc.) to certain weapon attacks...obviously they would be limited, due not being able to use them every round endlessly like a rogue, and you have a limited amount to use, but it gives the flavor. This would make it not OP too, because you will really need to think, do I use 4 points for this, or save some for twin spell? Since this becomes a super point use build, if you kill something with this skill, you get the points back. anyhow there are lots of possibilities to make this work and not be OP.
Basically you need to start your subclass within a full magic user...then make the subclass give rogue like perks that are tied to mage abilities. Remember, casters are already powerful, so you can not give the full ability that a rogue has, or they will be WAY to OP...and their rouge damage or abilities, can not out do rogues...for balance, and the fact mages already are awesome.
EDIT: What I do is take levels of Arcane Trickster, until I get the amount of sneak attack die I want, then just do the rest of the levels Wizard...makes for a super powerful Rogue/Mage.
I usually only do 2 levels of Wiz on an Arcane Trickster. It doubles the Arcane part of the character while still maximizing the Rogue aspect. With green-flame blade, that’s a lot of damage on a hit, and with something like Divination or Bladesinger as the Wiz subclass it really works well, even with only the 2 levels.
Creating Epic Boons on DDB
DDB Buyers' Guide
Hardcovers, DDB & You
Content Troubleshooting