Combination artifacts assembled in campaigns

Yes, it is possible to assemble other combination artifacts in Shadow of Death. In "Fall of Sandro" in Unholy Alliance, you can trade in the Elixir of Life for other combination artifacts at a seer's hut underground. Here is a map of that mission:

Legend:

Green - Friendly Town

Red - Enemy Town

Grey - Neutral Town

Yellow - Underground Passage

A# - Allied Towns

O# - Opponent Towns (a,b,c,d,e,f,g indicates which enemy)

N# - Neutral Towns

M# - Mirror Entrances (a) and exits (b). two-way unless stated E# - Exit (a) entrance and (b) exit

S# - Seer(a) and the location of the item (b)

G# - Guard Tents (a) and the location of the Guard Tower (b)

J - Jail

X - Ambush

Source: https://www.celestialheavens.com/viewpage.php?id=307

There are seer huts not marked on the map in the other underground chambers, each one gives you a different combination artifact in exchange for the Elixir of Life (Which can be obtained in that mission). According to Celestial Heavens:

The Air Cave will give you the Power of the Dragon Father, the Fire Cave will give you the Wizard's Well, the Water Cave will give you the Ring of the Magi, and the Earth Cave will give you the Bow of the Sharpshooter.

Now, you can also assemble other combination artifacts outside of that mission. 90% of the artifacts on each of the maps are random, except for ones that have been specifically specified by the developers. In the first mission of "Elixir of Life" (Gelu's campaign), I have actually assembled the Ring of the Magi because one of the enemy heroes that was trapped underground had two of the three components, while I happened to get the other one. Unfortunately, I didn't get to put it to good use, since I was then able to finish the mission by capturing the last town.

Now, whether the components of the various combination artifacts will appear in YOUR playthrough of the campaign is heavily dependent on whether the developers chose to specifically exclude certain artifacts from appearing in a map and whether the RNG will spawn the needed components.

TL;DR: It all depends on luck.