How many US airports have 4 or more parallel runways?
Based on my current navigation database (AIRAC 1909, valid from 2019-08-15), I found 7 US airports with 4 (or more) parallel runways:


KATL (Hartsfield–Jackson Atlanta International Airport):
5 parallel runways: 08L/26R, 08R/26L, 09L/27R, 09R/27L, 10/28
KDEN (Denver International Airport):
4 parallel runways: 16L/34R, 16R/34L, 17L/35R, 17R/35L
and 2 more parallel runways: 07/25, 08/26
KDFW (Dallas/Fort Worth International Airport):
5 parallel runways: 17L/35R, 17C/35C, 17R/35L, 18L/36R, 18R/36L
and 2 more parallel runways: 13L/31R, 13R/31L
KDTW (Detroit Metropolitan Airport):
4 parallel runways: 03L/21R, 03R/21L, 04L/22R, 04R/22L
and 2 more parallel runways: 09L/27R, 09R/27L
KLAX (Los Angeles International Airport):
4 parallel runways: 06L/24R, 06R/24L, 07L/25R, 07R/25L
KMCO (Orlando International Airport):
4 parallel runways: 17L/35R, 17R/35L, 18L/36R, 18R/36L
KORD (Chicago O'Hare International Airport):
5 parallel runways: 09L/27R, 09R/27L, 10L/28R, 10C/28C, 10R/28L
and 2 more parallel runways: 04L/22R, 04R/22L


I do not know how many are planning additions, but I linked the Wikipedia article for each of the airports, maybe that will help you find more information on that.

Trivia: There are only 3 airports outside the US with 4 parallel runways: LFPG (Paris Charles de Gaulle Airport), LFTM (Istanbul Airport) and ZSPD (Shanghai Pudong International Airport).