user11144: Especially for checking studies (maybe also for teaching), it would be helpful to have an engine finding the second best move and assess it (or even give refutations of all alternatives). For a tablebase position, this is trivial. Can the Lichess/Stockfish engine do that? If not, do (especially online) alternatives exist?

user4399: I'm not the biggest fan of chess dot com. As a 9LX player I of course prefer lichess but even chess dot com has this.
Just click show lines to get

the following

Go to settings to adjust number of lines:


Btw this is how it looks like on lichess:
Just 1 line:

Find multiple lines:

The final product:


What surprises me in particular about OP's question is that multiple lines option helps show how sharp/critical a position is. Eg I loaded a puzzle on lichess and here's what I have:

The red circle/oval/ellipse shows the only good move for black (good here means winning, not winning-or-drawish). The orange box shows there are 2 drawish moves. Finally the blue box shows the (least) bad moves (meaning [the least] winning for white). This setup of arranging by least to greatest evaluation shows that any other move is bad

user15223: Yeah engines can do it. Here's how you do it on Lichess:

Then when you run the analysis the engine gives three moves. You can increase the number of lines you want as well, which can be a waste since in this particular position, Black really only has one good move (...g6) so resources spent analyzing the 2nd-best (...Ke7) and 3rd-best (...Qf6) moves are wasted.

11144: <p>Especially for checking studies (maybe also for teaching), it would be helpful to have an engine finding the second best move and assess it (or even give refutations of all alternatives). For a tablebase position, this is trivial. Can the Lichess/Stockfish engine do that? If not, do (especially online) alternatives exist?</p>
 4399: <p>I'm not the biggest fan of chess dot com. As a 9LX player I of course prefer <a href="https://chess.stackexchange.com/a/37401">lichess</a> but even chess dot com has this.</p>
<p>Just click show lines to get</p>
<p><a href="https://i.stack.imgur.com/Rt4rq.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Rt4rq.png" alt="enter image description here" /></a></p>
<p>the following</p>
<p><a href="https://i.stack.imgur.com/s7oUl.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/s7oUl.png" alt="enter image description here" /></a></p>
<p>Go to settings to adjust number of lines:</p>
<p><a href="https://i.stack.imgur.com/N7zfs.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/N7zfs.png" alt="enter image description here" /></a></p>
<hr />
<p>Btw this is how it looks like on lichess:</p>
<p>Just 1 line:</p>
<p><a href="https://i.stack.imgur.com/qntVA.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/qntVA.png" alt="enter image description here" /></a></p>
<p>Find multiple lines:</p>
<p><a href="https://i.stack.imgur.com/Gpr9Z.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Gpr9Z.png" alt="enter image description here" /></a></p>
<p>The final product:</p>
<p><a href="https://i.stack.imgur.com/HuiNr.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/HuiNr.png" alt="enter image description here" /></a></p>
<hr />
<p>What surprises me in particular about OP's question is that multiple lines option helps show how sharp/critical a position is. Eg I loaded a <a href="https://lichess.org/training/5Bypy" rel="nofollow noreferrer">puzzle</a> on lichess and here's what I have:</p>
<p><a href="https://i.stack.imgur.com/fVFUC.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/fVFUC.png" alt="enter image description here" /></a></p>
<p>The red <a href="https://math.stackexchange.com/questions/2249741/why-do-we-have-circles-for-ellipses-squares-for-rectangles-but-nothing-for-tria">circle/oval/ellipse</a> shows the only good move for black (good here means winning, not winning-or-drawish). The orange <a href="https://matheducators.stackexchange.com/questions/13700/in-what-curricula-are-rectangles-defined-so-as-to-exclude-squares">box</a> shows there are 2 drawish moves. Finally the blue box shows the (least) bad moves (meaning [the least] winning for white). This setup of arranging by least to greatest evaluation shows that any other move is bad</p>
 15223: <p>Yeah engines can do it. Here's how you do it on Lichess:</p>
<p><a href="https://i.stack.imgur.com/q8pGH.png" rel="noreferrer"><img src="https://i.stack.imgur.com/q8pGH.png" alt="enter image description here" /></a></p>
<p>Then when you run the analysis the engine gives three moves. You can increase the number of lines you want as well, which can be a waste since in this particular position, Black really only has one good move (...g6) so resources spent analyzing the 2nd-best (...Ke7) and 3rd-best (...Qf6) moves are wasted.</p>
