You can catch a teammate after they catch the ball to keep them from getting injured. Even if an opposing player tried to catch someone to keep them from getting injured, this is fair - umpires call on intent.
Now if a teammate assists/helps before the catch is made I am calling interference every single time. It is simply "interference" which can be called on an out or safe call and can go either way.
The section below is included in the definition of a catch in the MLB rulebook:
(Catch) Comment: A catch is legal if the ball is finally held by any
fielder, even though juggled, or held by another fielder before it
touches the ground. Runners may leave their bases the instant the
first fielder touches the ball. A fielder may reach over a fence,
railing, rope or other line of demarcation to make a catch. He may
jump on top of a railing, or canvas that may be in foul ground. No
interference should be allowed when a fielder reaches over a fence,
railing, rope or into a stand to catch a ball. He does so at his own
risk. If a fielder, attempting a catch at the edge of the dugout, is
“held up” and kept from an apparent fall by a player or players of
either team and the catch is made, it shall be allowed.
This is a very specific comment but just speaks to the line between assist and interference on a play. Also refer to Section 6.01(d) that is about Unintentional Interference. Most oddball cases of interference concerning players or coaches (not fans - which there is a clear rule for) fall under Unintentional Interference.
So as an umpire we know that coaches/players can act as a wall by dugout steps - which the quote above clearly instructs. But all umpires are instructed also that to use the Unintentional Interference rules to make decisions on things like this. If there was "help" before they catch it, then we don't know if it would have been caught or not. Therefore no catch. But that is the umpire clearly saying there was "help". It is really a judgement decision. I know that in MLB they are a lot more forgiving on this rule (maybe because players are worth a lot more) than they are in the college or high school games.
I personally have called a bunch of college games... I had one batted ball that went into the defenses dugout and players held him up - but beyond dugout stairs, and luckily for me he dropped it. I would have had to take the catch away because they clearly gave the player another couple of feet in the air - not formed a wall. Now if it was the opposing teams dugout as long as intent is good once you hit the dugout area even if their clumsiness caused the flyball I wouldn't label it interference unless it was intentional.
Also note - and maybe a great trivia question because maybe one of those things that has never happened in MLB - that if the opposing team assists too much to help a fielder it is also Unintentional Interference and umpires if doing their job by the book should call the play dead with no catch.