The question is usually asked as though there were a list, and somewhere there is a plant that would be fine and a plant that would not.
The published answer is less dramatic and more useful: nearly all of them can, provided they go into shade. Iowa State University Extension puts it as houseplants doing best when they "'vacation' in a full-shade or part-shade location outdoors", and notes that "many houseplants can be in full shade the entire summer."
So the interesting question is not which plants can. It is which ones are worth moving, and that turns out to depend on your balcony more than on the species.
Why the species matters less than you would expect
The reason is what these plants are:
"Nearly all houseplants are tropical understory plants. These plants are used to low light and warm temperatures, which is why they do so well in our homes."
They share an origin. Something that grew under a canopy will generally accept shade under a balcony, which is why the answer to "can it go out" is so often yes, and why the answer to "can it go into full sun" is so consistently no.
The one hard warning the source gives is not about a species people worry about. It is about the one they do not:
"Never move houseplants from indoors into full sun. Leaf burn, discoloration, and drop can occur. On some species, especially succulents, the damage to the fleshy stems and leaves is permanent."
Succulents, named specifically, permanent damage. Those are exactly the plants people are most confident about putting in the sun because they look like desert plants. If you take one thing from this page, take that one.
The four questions that actually decide it
Since the species answer is mostly yes, the decision comes down to your situation.
1. Do you have a shaded position? If your balcony is shaded, or has a shaded end, you have what the guidance asks for. If it is fully exposed all day, the source's answer is to provide shade with cloth or material, and if you cannot, this is a harder call for every plant rather than for particular ones.
2. Can you move it without damaging it? Size and weight matter more than hardiness here. A large plant carried through a doorway and down a step has a real risk of physical damage that has nothing to do with the outdoors.
3. Does it resent being moved? The source names weeping fig and tropical hibiscus as prone to leaf drop when moved, even with the gentlest transition, with new leaves emerging in a couple of weeks. That is worth knowing before you conclude you have harmed it.
4. How much does it stand to gain? This is the one nobody asks, and it is the most useful. A plant that spent winter in a dim position gains far more than one that spent winter on your brightest sill. The gap between its current conditions and outdoor shade is the size of the benefit.
So the ones worth moving first
Ranking by benefit rather than by tolerance:
Plants from your dimmest positions. Largest gain, and per the source, even a shady spot outdoors exceeds the brightest indoor position. If your best window faces north, what that band supports explains why almost everything in your home is a candidate.
Plants that are easy to carry. Because you will actually do it, and do it back in autumn.
Plants that have been in the same spot for a long time. A change of conditions is more valuable to them than to something you recently placed well.
And the ones to leave inside
Anything you cannot move without a helper, unless you have one.
Anything currently doing well in a good position. The gain is smallest and the risk of the round trip is the same.
Anything if your only outdoor position is exposed and you cannot shade it. That is the situation the permanent-damage warning is about.
Anything if the season is not long enough to repay the setup. The acclimation alone takes 10 to 14 days after nights are "consistently and reliably above 50°F", and if your usable window is short, that arithmetic can eat the whole trip.
What you cannot skip whatever you move
The sequence is the same for every plant: indoors, then outdoor full shade, then more light across 10 to 14 days, then the summer position, which for many plants is still shade.
There is no plant on the "can go outside" list that can skip that, and the plants people most want to skip it for, the sun-looking ones, are the ones the source warns about by name.
Check individual species yourself
I am not giving you a list, and that is deliberate rather than lazy. Verifying species one by one was not done here, and a list assembled from general impression is exactly the kind of thing that gets copied around and acted on.
Check anything you are unsure about by botanical name, on a university extension page or the grower's own material. The general rule from the source covers most cases; the exceptions are worth looking up rather than guessing.
If you have pets
The balcony is where animals sit in warm weather, and plants there are at floor and rail height. Check anything you move, by botanical name, against the ASPCA's toxic and non-toxic plants database.
Frequently Asked Questions
Which houseplants can go outside for the summer?
Nearly all of them, provided they go into shade. Iowa State University Extension says houseplants do best when they vacation in a full-shade or part-shade location outdoors, and that many can be in full shade the entire summer. The reason the species matters less than people expect is that nearly all houseplants are tropical understory plants, used to low light and warm temperatures, which is why they do so well in our homes.
Are succulents safe to put in full sun outdoors?
This is the one hard warning in the source, and it lands on the plants people are most confident about. Iowa State says never to move houseplants from indoors into full sun, because leaf burn, discoloration and drop can occur, and that on some species, especially succulents, the damage to the fleshy stems and leaves is permanent.
How do I decide which of my plants to move?
By benefit rather than by tolerance. Move the plants from your dimmest positions first, since even a shady spot outdoors exceeds the brightest indoor one, so the gap they close is largest. Move the ones you can carry easily, because you will actually do it and do it back in autumn. And favor plants that have sat in the same spot a long time, since a change of conditions is worth more to them.
Which plants are better left indoors?
Anything you cannot move without a helper. Anything already doing well in a good position, because the gain is smallest and the round trip carries the same risk. Anything at all if your only outdoor position is exposed and you cannot shade it, which is the situation the permanent-damage warning describes. And anything if your season is too short, since the acclimation alone takes 10 to 14 days after nights are consistently and reliably above 50°F.
My plant dropped leaves after I moved it. Have I damaged it?
Not necessarily. Iowa State notes that some indoor plants, like weeping fig and tropical hibiscus, are prone to leaf drop when moved to a new location even with the gentlest transition, with new leaves emerging in a couple of weeks. Burning or discoloration is the signal that means the light is too intense; leaf drop on a species known for it is a plant adjusting.
The part worth remembering
Almost all houseplants can go outside, into shade. Very few should go into sun, and succulents are named as the ones where the damage does not reverse.
So choose by benefit rather than by tolerance: the plants from your dimmest positions, the ones you can carry, and the ones you will remember to bring back in. If you have not yet worked out which of your positions are the dim ones, the room-by-room survey is where that starts.