So, let's say that somehow, someway, Kirk and Co. find themselves on LV-426 during the events of Aliens (1986). The crew encounters a distress signal and, due to plot interference, their transporters don't work. Kirk orders a shuttlecraft down to the colony to investigate. Later, they find that the atmosphere is also interfering with their communicators -- they can talk to each other, but not the Enterprise, at least not without a more powerful radio. In essence, they've replaced Ripley, Burke, and the Marines.
The landing party consists of the senior staff: Kirk, Spock, McCoy, Scotty, Sulu, Uhura, Chekov. They have their phasers, tricorders, communicators, and standard equipment (i.e. McCoy with his medicine bag, Scotty with his toolkit, etc).
From here on out, the rest of the movie plays out normally, including the power plant. Can our heroes find (but not rescue!) the colonists, defeat the Queen, and return to the Enterprise? Each round is a separate scenario, and the first time the crew meets the Xenomorphs.
Round 1: The crew circa Season 3 of TOS
Round 2: The crew (with Chekov and Spock) circa The Wrath of Khan (with bonus James Horner score)
Round 3: The NuTrek crew after the events of Beyond
Bonus: using standard equipment, how do casts of the other shows fare?