Part I of "Magic Doesn't Stack" really only covered magical defenses: armor bonuses, shield bonuses, Protection from Evil spells, and Ring of Protection. I didn't address attack bonuses at all.
OD&D is short on "buff" spells seen in later editions, so it's hard to judge whether the rules intended for attack bonuses to stack at all. The only spell in Men & Magic that adds to the attack roll of a weapon-wielding combatant is the Bless spell. There's no explicit exemptions, so it might stack.
There's an interesting distinction between various magic weapons:
- Swords add their bonus to the attack roll, but rarely the damage roll.
- Bows and Arrows add the total magic bonus to the attack roll, so they do stack. Only arrows add to damage.
- Other weapons only increase damage; they do not have an attack bonus.
The only non-weapon magic item mentioned as increasing attack probabilities is the Girdle of Giant Strength. Not the Gauntlets of Ogre Power, which are specifically exempted (they increase damage, not attack capability.) However, the Girdle doesn't have an attack bonus; it gives the wearer the attack capability of a Hill Giant. I take this to mean that low-level characters who wear a Girdle of Giant Strength attack as an 8 HD monster, while Fighters of 9th level or higher, or very high level patriarchs or wizards, gain no benefit.
Given these, it would be very easy to just rule that attack bonuses don't stack, either. But I think it's reasonable to allow one weapon bonus and one non-weapon bonus to stack. Plus, the ability score bonus (Dex, for ranged weapons in the 3LBBs) and the best situation bonus (like attacking from the rear) seem reasonable, too, although I'm not sure yet whether the ability score bonus should be treated as a situation bonus.
The reason for the limits is, of course, to avoid bonus inflation. Bless gives a +1, the best magic weapon gives a +3. There are few situational modifiers listed in the 3LBBs, but Greyhawk mentions a +4 to attack from the rear. That gives a +7, which seems like a lot. I wouldn't want to go much higher than that.