Sure, your sentence is ok. I assume it means:

This person looks nothing like you — nor like anyone, for that matter.

Not all instances of nor need be paired with neither. Here are citations from the OED demonstrating this:

• A. 1586 Sidney Arcadia (1613) 41 - She concealed her sorrow, nor cause of her sorrow, from no body.
• 1590 Spenser F.Q. i. iii. 11 - She could not heare, nor speake, nor understand.
• 1591 Shaks. Two Gent. v. iv. 80 - Who by Repentance is not satisfied, Is nor of heauen, nor earth.
• 1622 Wither Philarete (1633) 617 - No others high degree, Nor beauteous looke shall change me.
• 1631 May tr. Barclay’s Mirr. Mindes i. 39 - The whole coast is most sweetly verdant,..nor hardly, is there ground any where more abundantly fruitfull.
• 1667 Milton P.L. iii. 626 - A golden tiar Circl’d his Head, nor less his Locks behind..Lay waving round.
• 1688 Holme Armoury iii. 251/2 - It is said of the French that they Speak not as they Write, nor Write as they Speak.
• 1766 Goldsm. Vic. W. i, - We had no revolutions to fear, nor fatigues to undergo.
• 1788 Trifler No. 22. 291 - The little creature cried and laid down, nor could all our beating raise it.
• 1791 Mrs. Radcliffe Rom. Forest x, - Your father nor nobody else has ever sent after you.
• 1798 Coleridge Anc. Mar. i. xiv, - Nor shapes of men nor beasts we ken.
• 1807 J. Barlow Columb. iii. 349 - But we nor fear his frown, nor trust his smile.
• 1821 Byron Heaven & Earth iii. 673 - Away! nor weep!
• 1821 Scott Pirate Adv., - The inhabitants..not possessing arms nor means of resistance.
• 1870 Gladstone Glean. (1879) IV. 252 - Not a vessel, nor a gun, nor a man, were on the ground to prevent their landing.
• 1875 Jowett Plato (ed. 2) I. 423 - Nor among the friends of Socrates must the jailer be forgotten.

For more recent examples, we have this line from Christopher Tolkien’s introduction to his father’s Silmarillion:

• But it was never published (though some indication of its content could be gleaned from The Lord of the Rings), and throughout my father’s long life he never abandoned it, nor ceased even in his last years to work on it.

And this from his father’s introduction to The Lord of the Rings:

• It is perhaps not possible in a long tale to please everybody at all points, nor to displease everybody at the same points; for I find from the letters that I have received that the passages or chapters that are to some a blemish are all by others specially approved.

Those are pretty typical uses, but there are many others. Here for example are a few from Gene Wolfe’s Book of the New Sun:

• Stone is not too hard nor mud too soft.
• Yet it was not any of these things, nor the noctilucent light that clung to their fur, that brought the horror I felt.
• Why should these loyal workers starve so that murderers shall not die, nor thieves feel any pain?
• It had been a rule among the torturers that one should not speak to a client, nor understand anything a client chanced to say.
• The shouts of the cherkajis were no more, nor the shrill, mad cries that had come from the checkerboard of Ascian infantry.
• I could not find her, nor even the crimson-shot orange disk of the old sun.
• The true lines are not writing, nor speech either.

And here from George Martin’s Song of Ice and Fire:

• Past here, there were no hills, no mountains, no trees nor cities nor roads, only the endless grasses, the tall blades rippling like waves when the winds blew.
• Savage beasts he did not fear, nor any man who had ever drawn breath, but the sea was a different matter.
• It would not be the first time, nor the last.
• His hands had not been so steady for years, nor half so fluid.
• And he would never walk, nor fly, nor be a knight.
• No one had died of thirst while she was gone, nor even noted her brief absence.

And finally, from J.R.R. Tolkien:

• Immortal were the Elves, and their wisdom waxed from age to age, and no sickness nor pestilence brought death to them.
• But Fingon could not release the hell-wrought bond upon his wrist, nor sever it, nor draw it from the stone.
• He had not forgotten the look of the Mountain, nor the thought of the dragon, and he had besides a shocking cold.
• And still there was no sight nor sound of Smaug.
• But also he did not reckon with the power that gold has upon which a dragon has long brooded, nor with dwarvish hearts.
• There was, however, no sign nor mention of money or jewellery: not a penny-piece or a glass bead was given away.
• ‘For mithril,’ answered Gandalf. ‘The wealth of Moria was not in gold and jewels, the toys of the Dwarves; nor in iron, their servant.’
• It is a great company on foot; but I cannot say more, nor see what kind of folk they may be.
• There was no sign of enemies nor of any challenge.
• He had not come, nor any of your Company, when I set out six days ago.
• ‘There were no dwarves nor children,’ said Éomer.
• There was no gleam of stone or gold, nor any fair thing in all their gear and harness: nor did their riders bear any badge or token, save only that each cloak was pinned upon the left shoulder by a brooch of silver shaped like a rayed star.
• My time is over: it is no longer my task to set things to rights, nor to help folk to do so.
• No one gets in nor out of it now.

I do not know the source of this pernicious myth that nor cannot ever occur unless paired with neither, but it is just that and nothing more. It has never been that way, nor is it now.

I blame Microsoft for this folly. :)

Edit

Here are sentences that actually begin with Nor. The interesting thing to consider is that many of these could be a continuation of a longer sentence, with a comma before the coördinating conjunction. These are from all three previously mentioned sources, sorted together for amusement and unpuzzling:

• Nor at all with the people of the Elvenking, whom I remember with small kindness.
• Nor can the Valar take away the gifts of Ilúvatar.
• Nor could he when the soldiers passed, nor the merchant with his wealth, nor the woman, for unenlightened men desire all those things, and the muni would have thought him one more such man.
• Nor could I have dreamed the heteroclite crewmen I had met aboard Tzadkiel’s ship, nor the jibers; and yet both had come from Briah, even as I; and Tzadkiel had not scrupled to take them into his service.
• Nor could such an instinct have developed slowly, a thousand generations of hawks fetching one stick before some hawk fetched two; because neither one stick nor two could be of the slightest use to the nesting hawks.
• Nor could the stronghold of Morgoth be ever wholly encircled: for the Iron Mountains, from whose great curving wall the towers of Thangorodrim were thrust forward, defended it upon either side, and were impassable to the Noldor, because of their snow and ice.
• Nor could they get away just now, as Thorin had pointed out.
• Nor could we fight against so many.
• Nor dare to shirk, While Goblins quaff, and Goblins laugh, Round and round far underground Below, my lad!
• Nor did he.
• Nor did he forget his words before the throne of Manwë.
• Nor did I desire Jolenta, who lay upon her side and snored.
• Nor did I know whether there were other buildings in addition to the principal one (a barbican, for example), or whether the wall was strengthened with towers or turrets, or how many defenders it might have.
• Nor did I see Abaia, their master.
• Nor did I see any sign of human pillagers, although there were animal droppings and a few feathers and scattered bones.
• Nor did Sam find any nook or hollow to shelter in: only bare stony slopes frowned over by the cliff, which now rose again, higher and more sheer as they went back.
• Nor did the Eldar desire to hasten, for they were filled with wonder at all that they saw, and by many lands and rivers they wished to abide; and though all were yet willing to wander, many feared rather their journey’s end than hoped for it.
• Nor did they hear or feel him trotting along well behind their torch-light as they led off their prisoners into the forest.
• Nor did they see them.
• Nor do I think that we should succeed, if we tried.
• Nor do I wonder that the Pelerines revered it.
• Nor do you.
• Nor Erebus, nor any other such monstrous thing.
• Nor ever again, one would think under this cloud.
• Nor had she any of that spirit that animates the members of a group forwarding the group’s purpose.
• Nor have you tried to take from me what you once sought.
• Nor in all my realm shall it be openly spoken, while my power endures.
• Nor is it always evil to die in battle, even in bitter pain.
• Nor is this town in the Wood-elves’ realm.
• Nor shall anything of my realm endure that a son should inherit.
• Nor shall I be passing Old Man Willow’s house this side of spring-time, not till the merry spring, when the River-daughter dances down the withy-path to bathe in the water.
• Nor shall I forget finding you on the hill of the last battle.
• Nor was he a young one, but simply a man in essence, a man freed of the gyre of time.
• Nor was I sure I wished to hear it.
• Nor was I wrong; for the space of a heartbeat we stared at each other, slayer and slain by both accounts.
• Nor was Piaton grafted to me.
• Nor was there any bolt of violet energy a moment afterward.
• Nor was the ship lost; it was indeed so near that I could see a sailor here and there in the rigging.
• Nor were those screams the howlings of lunacy and the shrieks of agony, as ours were.
• Nor when the riddling words of our dream were debated among us, did I think of Isildur’s Bane as being this same thing.
• Nor will he count the heads of the enemy save with a sword.
• Nor will I kill her, as she knows.
• Nor will I remain in this house.
• Nor will your children, nor theirs.
• Nor would I surrender my broken whetstone, both because it recalled the green man, and because it would be only a tawdry gift here, where stones nearly as good lay among the young grass on every side.
• Nor would I wish to see so great a good run to nothing in the wild.

You can only use "nor" between two noun phrases if you have already introduced the negative. It is part of the "neither...nor" construct, which is negative form of "either...or". Strictly speaking, too, the form is only permissible when there are two options, but I have seen the count extended by repeating the "or/nor".

Further, don't fall into the double negative: "Neither ...nor.... can" NOT "Neither...nor... cannot...".

So your phrase should look something like "Neither Cummings Motors nor Smith Electric nor our subcontractors can be held liable".

Thinking a bit further, however, this looks like an excerpt from a piece of legal text; in that case there are probably more specialized grammatical structures ("legalese") that you should consider using.