Yes, Abyss Cave is one of the biggest inspirations of Mira Co Rescue. Noir Castle makes a few games with similar mechanics but feature fetishes that are more themed around tickling. Here is a link to their Twitter. Abyss Cave also got a recent English Translation which makes it even more accessible for everyone. Their other game, Divirtual!, features two characters as well vs their more recent title that only has one character. You can find links to their games being sold on their pinned post of their latest game scheduled for mid August this year.
The other game with more 'rescue' related mechanics would be Moral Sword Asagi made by Ahriman. Their twitter page has their DLSite link listed in their profile. That game features four characters with various bondage related perils and such. Other games would include Marimo's games such as Sneak In Desperada and Signal Forces. Fair warning though, they do a lot of ryona and harder fetishes. These examples are similar but not identical in mechanics though, just inspirations.