For +2 to summoning skill you don't need a ilvl40, you need alvl (affix level) 40+ or in this case since we want the best possible item, you want alvl50 or more to get +2 to necromancer and not just +2 to summoning skill.

Now, you also need a ilvl<25 shrunken heads to be able to spawn a tier1 staff mod like raise skeleton and skeleton mastery, so at first glance this seems like a problem, but luckily the alvl is not calculated just with the ilvl there are others factors, there is the complete formula, I will explain it step by step since is a bit complicated:

If (ilvl>99) then {ilvl=99} 1
if (qlvl>ilvl) then {ilvl=qlvl} 2
if (magic_lvl>0) then {alvl=ilvl+magic_lvl} 3
else
{
if (ilvl<(99-qlvl/2)) 4
then {alvl=ilvl-qlvl/2}
else {alvl=2*ilvl-99} 5
}
If (alvl>99) then {alvl=99} 6

1: our ilvl is going to be low since it needs to be <25 so we skip step 1.
2: since we need a high alvl our qlvl need to be high so is going to be >25, so for now until the end of the formula, our ilvl = qlvl, this is only to get the +2 necro, for the staff mods we don't use this formula so changing our ilvl during this process is not going to alter that.
3: Magic level is something really weird that only orbs, staves and all four kind of circles have, so we skip this too.
4: Our new ilvl that is our qlvl is going to be > than 99-qlvl/2 so we go to step 5.
5: finally we know that alvl=2*ilvl-99 and we know that our ilvl=qlvl so, alvl=2*qlvl-99
6: Our alvl is not going to be > 99 so we also ignore this.

Since we need alvl50 we can change the formula to 50=2*qlvl-99, and we can deduce that our qlvl need to be >74 to be able to spawn a +2 necro skills even with extremely low ilvl.

There are only 2 shrunken head that have a qlvl>74 those are Succubus skull (qlvl81) or Bloodlord Skull (qlvl85) that means that those two are able to get +2 necro skill always not matter if they are ilvl1, the problem with those two, is that they don't drop at ilvl<25 or less naturally, so they can't get +3 Raise skeleton or +3 Skeleton mastery, so you need to lower their ilvl to be able to get that.

How do you do that? well, either you use the 6pskull recipe with a very low level char (a lvl1 char would lower the ilvl of the shrunken head already to ilvl15 with just 2 rerolls) and then you can keep rerolling it and try to be extremely lucky, or you just get a lvl8 char and imbued a shrunken head with that lvl8, that way you will have a ilvl12 shrunken head from the beggining and if you keep reroling with that lvl8 char you will eventually get stuck with a ilvl5 shrunken head that can spawn +3 to Raise skeleton since ilvl5<ilvl25 and +2 to necromancer skills since it will have alvl > 50.

And also since the ilvl is <12 you can't get any tier 3 or more staffmods raising a bit your chances to get the desirable staff mods.

So yes, +5 are possible, but you need to do some work before, only Succubus skull or Bloodlord Skull are able to spawn that (or Unearthed Wand and Lich Wand if you want to try it with wands) and still the odds are extremely low, just for reference a +2 necromancer +3 Raise skeleton rare shunker head with no other mods (I mean all other mods does not matter) is already more than 5 times harder to get than a JMoD, if you on top of that want a second staff mod like Skeleton mastery, resist, 2sox and stuff like that to make it really good, the odds are waaaay lower.

This post was edited by Titus1986 on Jan 3 2022 06:43am

Thanks for the info. So it's possible, but, for the record, no one has ever had one until proven otherwise. So since Succubus Skulls are level 60 required, how about +4 raise skeleton at level 30 or less?

https://forums.d2jsp.org/topic.php?t=78080117&f=103

That one is superclose, I mean, is a +5 to both raise and mastery, but with +2 summon and no +2 necro.

I'm pretty sure is not the only one in the history of D2, but for sure there aren't many out there.

For +4, Raise skeleton need a ilvl < 25 shrunken heads, many areas of normal has this, and +1 to summons is alvl20, so Preserved Head and Zombie Head can spawn that at ilvl24 since their qlvl is very low and they reach alvl20 just with the ilvl.

At that point tho, is easier to find a white shrunken head with +3 raise skeleton that any shrunken head can spawn as long as is ilvl < 25 and get a splendor for the +1 skill.