I'm in the process of negotiating something like this for maternity leave. My organisation offers very generous maternity benefits, but it offers them on an all or nothing basis - as the policy is currently written, I need to stay away entirely for a whole year, or I need to come back full-time. If I come back part-time, I lose a number of benefits that are valuable to me, including particularly benefits that protect the value of my existing retirement accounts. Although we can afford for me to take a year off, I've done this once before, and the problem is that the organisation has trouble honouring that arrangement - in practice, I end up working a substantial amount, while being paid only the benefits one is meant to receive while completely on leave.
This time around, what I want to do is formalise - and get paid for - a specific amount of specific kinds of work that I will continue to do while otherwise on maternity leave. I want to do this, while receiving the same benefits I would otherwise receive if I were not working at all. The benefits I want preserved have to do with how my "service fraction" is calculated - we have a provision whereby you continue to be counted as a full-time employee while on maternity leave for up to two years. You don't get /paid/ as a full-time employee, but you continue to accrue certain other benefits at a full-time pace, even though you are not working.
However, current policy is that, once you return to work, if you return part-time rather than full-time, your service fraction is immediately reduced due to your part-time hours. This strikes me as irrational - the incentive structure means that someone is better off not working at all, than working even a substantial number of part-time hours. It's also legally dubious (here).
So I'm requesting permission to negotiate part-time hours during the maternity leave period, without a reduction in the benefits I would receive if I weren't working at all. I'm also, incidentally, using it to gain greater control over what my job will be: basically, I want to keep all the parts I most like and that are the most flexible (research and research student supervision), while handing over the parts I find most tedious (administration) or that I like, but that require a rigid schedule that I don't want to maintain with a young baby (teaching).
My managers are thrilled - I'm highly skilled, research productive, and I supervise a large number of PhD candidates in a context where we're under increasing pressure to improve the timely completion rates for our PhDs. They are relieved that the area doesn't have to lose me entirely. So the conversation with them was fairly straightforward - I made a case for the work I wanted to retain (it helps that there is actually research to show that, when academic staff go on mat leave, their areas tend to backfill their teaching and admin, but leave their research work unfilled, because it's difficult to substitute one person for another in many research fields, particularly for a short duration). I had already mapped out for them who could take over the responsibilities that I want to surrender, so I had taken away most of the stress of planning how exactly this would play out. And I did it early enough that I could do a proper handover to those people, to minimise disruption for them (and the risks of my having to fend off calls from work when I'm on the labour ward). So that discussion boiled down to my being able to give them a very clear sense of how exactly it would work, and why they would benefit.
The various administrative parts of the university are... much less thrilled. For various reasons, mainly down to how our HR software works, it will cause a headache for HR to do this, and they are responding to that technical difficulty by posing all sorts of spurious objections: that it's not legal; that it violates OH&S regulations; that it would be damaging to my "work-life balance", that I birth/a young child/ etc., are too stressful for me to be able to combine them with these responsibilities, etc. Aside from being generally smarmy, many of their objections are frankly illegal (here). So with them it's been a more strategic and aggressive game of getting them to put what they're telling me into writing (they must have some sense they are in problematic territory, since they try to avoid doing this - I've had to screen their phone calls to force them to interact with me via email). Once that was done, I could hit them with very polite, well-researched, queries in the vein of "It sounds very much like you are saying X - but that can't be what you actually meant, because that would abrogate Y law. Could you clarify so that I'm sure I've understood." etc. It didn't take much of that to get much more ameliorating responses, as well as the escalation of my request higher up the HR food chain.
I've also done a quick sweep of policies of other universities, so I had a dozen best practice examples from competitor institutions that explicitly allow what I'm requesting.
I realise not all of this will apply - pregnancy and maternity are protected classes in many places, so employers have to tread more cautiously. But the approach of developing a clear plan, so that you've taken off the table objections that boil down to a panicked "Oh my god! How will we cope?", and presenting the whole thing as a clear win-win, and maybe starting with whichever level of management is most likely to be receptive, before moving on to the more problematic people, could help. Best practice examples from other institutions might be useful too, particularly if your organisation tries to market itself to existing or prospective staff - or clients or the general public - as progressive in some way.
There's also always the option of walking - and then letting them ask you to come back as a consultant, which gives you more ability to negotiate terms. If I weren't in a mat leave situation, that's actually what I would probably do here: I'd have an initial conversation, make a proposal, and "regretfully" leave, without burning bridges, and wait for them to ask me to come back and help out. I've never left a job where someone hasn't had to hire multiple people to replace me - generally, I've refused offers to return to help out because I really wanted out - but where I am now /could/ be a decent job, with certain tweaks, until I retire. So I'd be more open, here, to negotiating after leaving. I've had the impression from some of your other posts that you are also someone who's much more productive than the average staff member, so I'd think they'd be in the same position of needing to scramble around to replace you if you left entirely. This opens up a lot of potential, both to sell them on the idea of keeping you on your own terms, and to leave if necessary and see whether this changes their perspective on your original request.