You need to be "holding" the grimoire so most (if not all) DM's would require that to be in a hand. You cannot gain a bonus from more than one thing that is the same (item with same name or the same spell cast twice or similar) so one Wand of the War Mage only.
But you should be able to stack the wand and the grimoire though.
The DNDB character sheet (and my DM) will let you. Same with Amulet of the Devout (I have one level in cleric and 13 in wizard and it even works on wizard spells). Robe of Archmagi stacks too. But, you may run out of attunement slots. There is a Critical role feel that gives you another attunement slot. My spell DC is around 20 I think.
You would have to hold the Grimoire in one hand, so you could only hold one wand, but that’s okay because you can only benefit from one item at a time anyway since they have the same name.
Both items only require that you hold them, so yes their effects stack when a character is holding both of them. One thing to note is that this character now has no free hands. This is important because it becomes a problem when casting a spell with a Somatic component but no Material component. A hand holding a spellcasting focus can only provide the Somatic component of a spell when the spellcasting focus is being used to provide the Material component of a spell. This is also a problem when a spell has a Material component that either has a gp cost or is consumed by the spell. Because then a spell casting focus cannot be used to substitute for the Material component. In both of these scenarios the character will need to stow either the wand or the grimoire to free up a hand and cast the spell.
Unless they are a loxodon, thri-kreen, or plasmoid, then you have a trunk, two extra arms, or a pseudopod to hold the grimoir or whatever. Also, if you have one level in cleric (like my wizard does), you can use an amulet of the devout which is better than the wand of the war made (spell attack rolls AND dc and works on all your spells, not just cleric) and doesn't. require a free hand. also, the robe of the archmagi helps with a DC and spell attack increase of 2. You could also get that tome that raised your INT and INT MAX by 2 and go above 20 INT, which would help too. Also, if you need it CR has a feat that lets you attune to a 4th item.
Unless they are a loxodon, thri-kreen, or plasmoid, then you have a trunk, two extra arms, or a pseudopod to hold the grimoir or whatever. Also, if you have one level in cleric (like my wizard does), you can use an amulet of the devout which is better than the wand of the war made (spell attack rolls AND dc and works on all your spells, not just cleric) and doesn't. require a free hand. also, the robe of the archmagi helps with a DC and spell attack increase of 2. You could also get that tome that raised your INT and INT MAX by 2 and go above 20 INT, which would help too. Also, if you need it CR has a feat that lets you attune to a 4th item.
Being an Artificer could also help with that.
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Can a wizard hold an arcane grimiore in their arms and a wand of the war mage in each hand and stack the spell attack bonuses?
You need to be "holding" the grimoire so most (if not all) DM's would require that to be in a hand.
You cannot gain a bonus from more than one thing that is the same (item with same name or the same spell cast twice or similar) so one Wand of the War Mage only.
But you should be able to stack the wand and the grimoire though.
I don't think you can stack the attack bonuses at all, though the Wand would allow you to ignore half cover.
The DNDB character sheet (and my DM) will let you. Same with Amulet of the Devout (I have one level in cleric and 13 in wizard and it even works on wizard spells). Robe of Archmagi stacks too. But, you may run out of attunement slots. There is a Critical role feel that gives you another attunement slot. My spell DC is around 20 I think.
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You would have to hold the Grimoire in one hand, so you could only hold one wand, but that’s okay because you can only benefit from one item at a time anyway since they have the same name.
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Both items only require that you hold them, so yes their effects stack when a character is holding both of them. One thing to note is that this character now has no free hands. This is important because it becomes a problem when casting a spell with a Somatic component but no Material component. A hand holding a spellcasting focus can only provide the Somatic component of a spell when the spellcasting focus is being used to provide the Material component of a spell. This is also a problem when a spell has a Material component that either has a gp cost or is consumed by the spell. Because then a spell casting focus cannot be used to substitute for the Material component. In both of these scenarios the character will need to stow either the wand or the grimoire to free up a hand and cast the spell.
Unless they are a loxodon, thri-kreen, or plasmoid, then you have a trunk, two extra arms, or a pseudopod to hold the grimoir or whatever. Also, if you have one level in cleric (like my wizard does), you can use an amulet of the devout which is better than the wand of the war made (spell attack rolls AND dc and works on all your spells, not just cleric) and doesn't. require a free hand. also, the robe of the archmagi helps with a DC and spell attack increase of 2. You could also get that tome that raised your INT and INT MAX by 2 and go above 20 INT, which would help too. Also, if you need it CR has a feat that lets you attune to a 4th item.
Food, Scifi/fantasy, anime, DND 5E and OSR geek.
Being an Artificer could also help with that.