If you could turn any 1-player game into a 2-player (simultaneous) game

[Oloturia]

Another one: Micronaut One racing game.
(also could be interesting a co-op normal game)

[bluespikey]

Another vote for commando

It exists, its called Duet. (Though its not really). But Ikari Warriors is a good match.

[SteveSmith]

Splat with two zippys

If anyone can't wait for someone to create this on the Speccy, there is a PC version: https://stephensmith.itch.io/multiplayer-splat (by me ).

[XTM]

I think Brainstorm would have to be a co-op, as the score is increased/decreased whenever a ball moves into a coloured square, so it's not really attributable to any player. But I reckon it'd work well as you could work together to trap it.

If the game engine was slightly changed with unique colours assigned to the below it would work:
a colour for player 1 score increase
a colour for player 1 score decrease
a colour for player 2 score increase
a colour for player 2 score decrease

That would make it a bit like Chu Chu Rocket (well, that game is a bit more complex, but you can do bad things to other players in it).

Even cooler if the game had added stuff on the map, like little circles for each player that if the ball passed over one, it would temporarily add bad squares for the other player or good ones for oneself, for something like 15 seconds.

[animaal]

Wizball.

I loved that game back in the day and I recently saw on Youtube that the C64 (spit) version allows a second player to control the "cat". Genius! That would have been a great addition to the Speccy version. And probably easy to implement too, since the cat is playable by the player already. I wonder why the devs couldn't have done that. Maybe time pressures.

[Morkin]

If the game engine was slightly changed with unique colours assigned to the below it would work:
a colour for player 1 score increase
a colour for player 1 score decrease
a colour for player 2 score increase
a colour for player 2 score decrease

If it's PvP, you can 'trap' the ball in your colour, so you'd probably have need to allow an option for sabotage, like a smart bomb (maybe with cooldown) that shatters your opponent's lines.

It'd be like a game of family Monopoly on Christmas day, lots of dead arms

[firelord]

If we are talking about networking (or another way for each player to use different keyboard) It would be interesting to play games with many keys as roles.
Eg Starglider 2 we could have one player drive and the other fire/identify . Just like Star Trek crew. You could add a third player to stand and just give the orders without touching anything*.
You can do this even with Psion Flight Simulator...

*Imagine 3 guys in their 40s-50s to be in a small room sitting with 2 spectrums and the third one standing and giving orders!

[Joefish]

A grey +2 fitted with a ZX-VGA-JOY or ZX-HD can display two separate screens. It's just it obviously takes twice as long to render both of them, slowing a game down to half its usual pace. And you'd have to watch that one player's gameplay doesn't stall when the other player moves into a new room in any sort of flip-screen maze or mansion where the scene is rendered in a dedicated chunk of effort on entry.

Something like Elite or Battlezone or some Dambusters sim with a gunner turret might be fun in multiplayer. Maybe better if it was mission-based rather than free-roaming, so a focussed challenge could be presented to test both players.