Can an arcane focus boost spell attack or damage rolls?

Question

Is it possible for an arcane focus to boost spell attack or damage rolls? To act as a +1/+2/etc. modifier, like stronger physical weapons.

Answer 1

Absolutely it can!

A wonderful example of this is the Wand of the War Mage, (p. 212, DMG).

uncommon (+1), rare (+2), or very rare (+3)

While holding this wand, you gain a bonus to spell attack rolls determined by the wand’s rarity. In addition, you ignore half cover when making a spell attack.

There are multiple items already built into the game that give Focus’s more power than a traditional Focus normally would.

Examples:
A Warlock (once having taken the Improved Pact Weapon feature) and College of Swords Bard can both use their Melee weapons as focuses for casting spells.

Clerics and Paladins can both use their shields as spellcasting focuses.

All of these items can be magical in nature and potentially give pluses to your spell casting and/or attack/damage rolls.

While every class can have some form of empowered focus or weapon/item that may be used as a focus, not all will empower spells but many can. If there’s something more specific you’re looking for I’d recommend perusing the items currently made within 5E through D&D Beyond, or the core rule books that you have at your disposal.

Answer 2

Yes, from a Level 2+ Artificer

The Artificer is an official subplemental class, that can be found in Wayfinder's Guide to Eberron and Tasha's Cauldron of Everthing. The first being specific to the Eberron setting, while the last is a settingless book, that can apply to any D&D World.

On 2nd level Artificers learn a class feature called Infuse Item, which enables them to pick from a list of infusions and have a certain amount of these active on items of their choice. One of the infusions is the Enhanced Arcane Focus, which reads:

Item: A rod, staff or wand (requires attunement)

and

While holding this item, a creature gains +1 bonus to spell attack rolls [...]. The bonus increases to +2 when you reach 10th level in this class.

This enables an Artificer of 2nd level or higher to infuse any Arcane Focus that is either a rod, staff or wand with the ability to grand the wielder a +1, or at later levels +2 bonus to their spell attacks. This comes at the cost of one of their Infuse Items slots for the Artificer and one of their magic item attunement slots for the spellcaster using the focus.

Note that there is no restriction on who can attune to such an item, so you don't even have to be an Artificer yourself to get to use an Enhanced Arcane Focus. It's enough if you have another player in your group who is willing to infuse the item for you. Your DM could also decide that there is an Artificer NPC for you in your game that is willing to do this for you, at your DMs discretion this could be done for free, for a price in gold pieces (possibly even per day) or perhaps as a reward for a quest the Artificer asks you do to for them.

Answer 3

Yes, if you have a magic item that does that

The problem, is that the rules on PH p. 151 that describe arcane foci say:

An arcane focus is a special item— an orb, a crystal, a rod, a specially constructed staff, a wand-like length of wood, or some similar item— designed to channel the power of arcane spells

and you can read that to mean not any wand or staff can do that, only one designed to act as an arcane focus.

And none of the wands or staffs in the DMG says it is designed to channel the power of arcane spells, or that it can be used as an arcane focus. There also are several items that say they can explicitly, including the Astral Shard, which is a crystal. If any wand, staff or crystal had this capacity, there would be no need to say so. This has been discussed in great detail in Does every magic rod, wand, crystal, orb, and staff count as an arcane focus?.

Now, as you can see from the answers to that Q&A, not only is the overwhelming community consensus that you should allow such magic wands and staffs to be usable as an arcane focus, it also is the repeatedly documented designer intent that this is possible.

In addition, if your DM designed a magic item like an Orb of Fiery Death that said it can be used as an arcane focus and adds +3 to your spell attack rolls for firebolt, then that would of course work too.

By all means, if your DM allows it, use your magical wand as an arcane focus. We have been doing so in our group, and it has not caused any issues, to the contrary, we think it is much more fun this way. If your wizard finds an awesome wand of the war mage in their adventures, it would really suck if they could not use it as the wand they use for their focus, and instead would have to use a boring old normal wand, just because that one says it can be used.