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No worries - thanks again for your advice!

Thanks, that's really helpful. We're in Australia, close to Sydney. So it's a pretty temperate climate - the summer shade and winter sun we get through this tree both improve conditions in the house a lot. The approach Mick suggested sounds good to me. The other advice we've received was to cut the branches with potential rot back to the trunk, and that 'topping' the tree would make things worse (I guess by encouraging more growth down low?). I realise there's probably more than one way to skin the cat, but what would your thoughts be on that approach? I might try to dig out all soil and debris I can from the crotches today to see if I can find any actual rot - I guess the best approach might depend on that? Although I suspect it will be difficult to tell how much damage there is. I found a few blurry phone photos of the branch that came down about a year ago (attached below). It looked like soil and water (and roots from a sapling) had worked their way about 500 mm down into the crotch, splitting it from the trunk. It came down under its own weight (i.e. without wind). Thanks again!

We have a large, established liquidambar tree with many competing leaders (the trunk is ~1m (3') diameter but 2 m (6') from the ground it divides into 10 or so ~300 mm (12") diameter branches). I've attached some photos. It dropped a large branch about 1 year ago, exposing some obvious rot in the branch crotch. We are worried because many of the remaining crotches collect a lot of leaves and debris--several containing damp soil when you dig down into it, and with saplings of some other species growing in the soil in the crotch. A few of these remaining branches would land on the house if they fell. Other than this, the tree seems really healthy. We would really like to keep the tree--it gives great seasonal shade and really sets the vibe of the whole property--but we also worry every time there's a strong wind. Any advice on how best to manage the tree would be really appreciated. We've struggled to get a local arborists to assess the tree (the one who comes recommended isn't taking new work, and others seem to only quote for removal). For example: - Should we be removing whatever soil, etc. we can from the crotches? - Is there a way we can assess the extent of rot and risk? - Is heavy pruning an option (one arborist told us removing the top of all leaders would stress the tree too much)? - Is cabling, or some other reinforcement, an option? Thanks very much in advance!