I own two dachshunds and have a 2-story home. My office is upstairs and my dogs love to hang out with me. Dachshunds are notorious for developing bad backs, so I try to prevent them from climbing the stairs. I have a large, flat-bottomed, metal-reinforced, wicker basket inside which I've laid a very thin cotton blanket. My dogs know to lay on the blanket inside the basket, which I then pick up to carry them up or down the stairs. We always keep the basket near the stairs.
Prior to owning the basket, we used a large dog bed to carry both hounds, but it was much heavier and bulkier than the basket.
I'm fairly sure my dachshunds are heavier and larger than 3 chihuahuas; the tail and head of one of them hangs over either end of the basket unless she curls up, which she often does. You can check your local craft store for appropriately-sized wicker baskets, the availability and variety of which increase nearing Easter time.