Here's a list of the accent parameters (the options you get when searching for rhymes, such as rhoticity and Father-Bother) I currently plan on adding. Reply to let me know if there are any others you'd like, or if you'd find some of these more useful than others, so I can prioritise the work. I'll keep this list up-to-date with any that are planned, in progress, or finished.

• Merry-marry-Mary merger (with several different choices depending on which are merged.) This would allow the requirements behind such rhymes as 'marry 'em'/planetarium' to be made explicit. In the current rhyme database Mary and merry are merged (so I would have to go through manually and determine which words used which sound), and marry is split.
• Trap-Bath split because pass doesn't always rhyme with mass, nor does it necessarily rhyme with moss under the father-bother merger. These are currently merged, so again, they'd have to be split manually.
• Flapping, so that we can find rhymes like 'polluted' and 'all you did'
• Short-i schwa because apparently in accents other than my own, 'open' doesn't rhyme with 'hopin''. This has actually already been implemented, but I found some other issues related to it (for instance, the dictionary currently thinks that some words with the '-ising' spelling use a different vowel from the same words with '-izing' spelling, while they should be the same even without this new parameter) so I want to fix those first.
• G-dropping so that open will rhyme with hoping when the previous parameter is appropriately set. This one should be pretty easy to do.
• H-dropping because I know people are going to be searching for 'oranges' and 'door hinges'. (Another general improvement I plan to make is either creating special pages for expected searches such as 'orange', or adding in known examples manually, with attribution. Meanwhile, I've made a forum thread for it)
• The near-square merger so that Great Big Sea can have their conscience clear. Combined with the merry-marry-Mary merger (something which I suspect it rarely coincides with) this would give near-limitless rhyming power!

Panda/pander merger. In my experience, it correlates strongly with non-rhoticity (So that's where the r went! They tacked it on at the end of the word!), but it's apparently not a perfect correlation, otherwise I'd propose merging it into the existing rhoticity setting.

Once in a sandwich shop in Cambridge, Massachusetts, I heard a customer order a "lodge tuner." I suppose he wanted to tune his lodge. At Logan Airport in Boston one frequently hears overhead pages involving "Delter Aihlines."

Quote from: mtgordon on 29 October 2016

Panda/pander merger. In my experience, it correlates strongly with non-rhoticity (So that's where the r went! They tacked it on at the end of the word!), but it's apparently not a perfect correlation, otherwise I'd propose merging it into the existing rhoticity setting.

The current non-rhotic setting does include pander as a rhyme for panda. To have this as a separate thing there could be either a separate panda/pander parameter, or one or two extra Rhoticity settings ('non-rhotic except for panda/pander', and 'rhotic except for panda/pander'.)

Quote from: mtgordon on 29 October 2016

Once in a sandwich shop in Cambridge, Massachusetts, I heard a customer order a "lodge tuner." I suppose he wanted to tune his lodge. At Logan Airport in Boston one frequently hears overhead pages involving "Delter Aihlines."

Delter Aihlines is non-rhotic with an intrusive R, and I suppose the same is true of 'lodge tuner' (with bonus father-bother merger) as well, though I'm not sure if it's called an intrusive R if there's nothing after it. I used to be amused by the 'alleluia ralleluia' while people were singing hymns in New Zealand.

I could perhaps add a setting for intrusive Rs, but I'm still trying to figure out what to do with the R that appears in the pronunciation of panda (or some other word ending in a vowel) when it is followed by an R word (which gives 'panda' two pronunciations, with the same rhymes all up but the rhoticity setting switched.)

Come to think, I suppose there are two distinct forms of panda/pander merger: merely non-rhotic (both sound to me like panda), and intrusive R, whether rhotic or not (both sound to me like pander). It's just that intrusive R is, in my experience, typically associated with non-rhotic accents.