The game I ran last night the Wizard used Levitate spell to move a paralyzed party member to a safe ground that was 30 feet above from their current location.

The discussion that came up is if the 20 feet indicated in the spell is the so-called 'ceiling' or does the text in the next paragraph mean that every turn you could raise the levitated object another 20 feet?

I ruled it as a 20 feet 'ceiling' and could not raise the object any high and the rule in the second paragraph means that the object can change hits height as directed by the Wizard only within an upper and lower range. 

One creature or loose object of your choice that you can see within range rises vertically, up to 20 feet, and remains suspended there for the duration. The spell can levitate a target that weighs up to 500 pounds. An unwilling creature that succeeds on a Constitution saving throw is unaffected.

The target can move only by pushing or pulling against a fixed object or surface within reach (such as a wall or a ceiling), which allows it to move as if it were climbing. You can change the target's altitude by up to 20 feet in either direction on your turn. If you are the target, you can move up or down as part of your move. Otherwise, you can use your action to move the target, which must remain within the spell's range.

When the spell ends, the target floats gently to the ground if it is still aloft.

The text says you can move up or down by a maximum of 20' per round. So, getting someone to 30' takes two turns.

Quote from Voras >>

The text says you can move up or down by a maximum of 20' per round. So, getting someone to 30' takes two turns.

Thanks!  Yeah, I understand that part of the additional turns with your clarification but as I mentioned in the OP I was just not sure if that 20 foot was the maximum hight limit overall for the spell.

60 ft. is the maximum range for the spell for determining eligible targets initially. However, a spells effect on the target doesn't end when it moves out of that distance unless the spell states so.

Otherwise, you can use your action to move the target, which must remain within the spell's range.

For an object or unconscious body the spell says so. :)

Quote from Voras >>

 

Otherwise, you can use your action to move the target, which must remain within the spell's range.

 

For an object or unconscious body the spell says so. :)

 Yeah, the Ranger did not appreciate being tethered around like a ballon.

Quote from Voras >>

 

Otherwise, you can use your action to move the target, which must remain within the spell's range.

 

For an object or unconscious body the spell says so. :)

No, that doesn’t say the spell ends when a target goes out of range. It says the caster can’t use their action to move the target beyond the spell’s range.

Quote from SagaTympana >>

Quote from Voras >>

 

Otherwise, you can use your action to move the target, which must remain within the spell's range.

 

For an object or unconscious body the spell says so. :)

 

No, that doesn’t say the spell ends when a target goes out of range. It says the caster can’t use their action to move the target beyond the spell’s range.

 So at 61 feet the target player who has the spell cast on them is pretty much 'space-walking'; ie, using fixed objects to move their given movement.  

Could a character with the spell cast upon them be raised say 40 feet be able to perform range attack action?

Assuming they were conscious, sure. 
I, personally, wouldn’t think too much about the physics behind it, though. Like how firing a crossbow might propel you in the opposite direction, or how it would be more difficult to fire a longbow since you wouldn’t be stabilized without you feet on the ground. (It might not be the case that it would matter, I’m no scientist, but it seems like it might matter) Some people might want to get into that, I’d just let them shoot, and be shot at in return. 

Hold up. Why are we assuming 60ft is the maximum height? That's the max range the spell can be cast from, and that is universally true for all spells with a casting range.

Levitate has a ceiling of 20 ft, per the opening line.

• Target is up in the air at 20 ft? You can move them down up to 20 ft with an action.
• Target is down at 0 ft? You can move them up to 20 ft with an action.
• Target is somewhere between 0 ft & 20 ft? You can move them within that range with an action.

It's Levitate, not Fly.

Quote from Sigred >>

Hold up. Why are we assuming 60ft is the maximum height? That's the max range the spell can be cast from, and that is universally true for all spells with a casting range.

Levitate has a ceiling of 20 ft, per the opening line.

• Target is up in the air at 20 ft? You can move them down up to 20 ft with an action.
• Target is down at 0 ft? You can move them up to 20 ft with an action.
• Target is somewhere between 0 ft & 20 ft? You can move them within that range with an action.

It's Levitate, not Fly.

 Sigred, the spell has an opening move of up to 20 feet, but the following phrase 

The target can move only by pushing or pulling against a fixed object or surface within reach (such as a wall or a ceiling), which allows it to move as if it were climbing. You can change the target's altitude by up to 20 feet in either direction on your turn. If you are the target, you can move up or down as part of your move. Otherwise, you can use your action to move the target, which must remain within the spell's range.

indicates that there is no restriction for movement after that other than 20 feet a turn and within the range of the spell.  So you can levitate a creature over 20 feet total, but it would take multiple turns to do so and you can’t exceed 60 feet away from you (assuming you’re right below the target)

It is Fly - but only vertically (not laterally) and very slow. Absolutely they can continue to go up 20 ft every turn so long as they remain within 60 ft of the caster.

Quote from Emmber >>

It is Fly - but only vertically (not laterally) and very slow. Absolutely they can continue to go up 20 ft every turn so long as they remain within 60 ft of the caster.

I don't agree with the condition. The only place the target having to remain in range is mentioned is specifically in relation to the caster using their action to move the target. In the other case of the target moving themselves, which to be fair they can do "only by pushing or pulling against a fixed object or surface within reach (such as a wall or a ceiling), which allows it to move as if it were climbing," there's no need to remain within 60 feet.

Sorry if this feels like nitpicking your language, but I feel like it's an important distinction to make. You can make them go up 20 feet every turn so long as they remain within 60 feet of you, yes, absolutely. But "they can continue" to do whatever with no such restriction.

Yea I should have mentioned I meant in regards to the caster using their action.

It reads like two people wrote it.