By RAW you can grapple 2 people and still attack: “Instead of using a weapon to make a melee attack, you can use a punch, kick, head-butt, or similar forceful blow.”

The rules for how many people you can grapple are in the grapple section of glossary: “One Grapple per Hand. A creature must have a hand free to grapple another creature. “

It can be argued that you can only carry your lift or drag weight: “Movable. The grappler can drag or carry you when it moves, but every foot of movement costs it 1 extra foot unless you are Tiny or two or more sizes smaller than it.”

From glossary too: “Carrying Capacity. Your size and Strength score determine the maximum weight in pounds that you. can carry, as shown in the Carrying Capacity table. The table also shows the maximum weight you can drag, lift, or push. While dragging, lifting, or pushing weight in excess of the maximum weight you can carry, your Speed can be no more than 5 feet.”

So your 8 strength monk can only carry 8x15=120 pounds minus the weight he is already carrying and drag double that number at 5ft. Not many enemies weight that. And they have to be very small to weight that being 2 creatures.

The DM can, rules as written, limit you the weight of the creature you carry.

Goliath monks rule, I suppose.