The tougher thing is that it's not quite like the NFL where those teams have so many positions to fill. It'd be easier to find a team willing to move down for multiple picks.
Typically with the NHL, the team trading down is doing so because they think they can still land their intended target. Teams generally don't move down for draft capital (arguably Sharks 2022 did, new GM inherited a mostly barren prospect cupboard).
So it's not quite as easy as finding a draft pick value chart and offering up enough "value." Teams will reference their own value charts, but usually it's predicated on whether they'd risk drafting a particular prospect or two.
Some post-lockout examples:
2005: Sharks offered something around #12 and #35 to Columbus for #6 but were turned down. They eventually traded #12, #49, and #207 to Atlanta for #8.
2007: St. Louis badly wanted Jakub Voracek but they knew he wouldn't slip to them at #9. They offered #9 and #24 to Edmonton for #6 but were turned down. There was a perceived top seven that year and Edmonton didn't want to move down.
LA mentioned that they had offers for #4 but didn't want to move down too far and miss out on Thomas Hickey. So they stayed put and reached for Hickey.
St. Louis pivoted and looked to trade down as their next target after Voracek was Lars Eller. They figured they could move down a few spots and still get Eller. Eventually they dealt #9 to San Jose for #13, #44, and 87. San Jose knew they had to leapfrog Florida at #10 for Logan Couture.
2008: Garth Snow went in with the mentality to trade down for multiple picks and apparently were targeting Josh Bailey. Moved from #5 to #7, then dealt #7 to Nashville for #9 and #40.
2019: Arizona traded #14 and #45 to Philadelphia for #11. Arizona apparently had Victor Soderstrom ranked in their top 5.