I did an old one once, not sure how old , but it was huge and growing in a very ugly shape, so, using my loppers, I took it down to about 6/8 inches all over at this time of year. To my surprise, it grew back very well... If they're really old, its a bit of a risk, but to be honest, the one I did looked so ghastly and was taking up so much space in a small border, it was worth the risk... I assume you mean Choisya when you say mexican orange...

If it is choisya then yes you can cut it back hard. if you wait till after it has flowered it will green up again in time for the autumn/winter. if you do it now you may get flowers later in the year or it may skip a year.

If the plant has sentimental value then remove about 1/3 of the branches down to 12" evenly round the shrub then do the same the next yre and then the final 1/3 the year after. then it will just need anuual tidying up after that.

welcome to GoY too :o)

Yes agree don’t be afraid to cut back hard they always come back, I have done these countless times over the years, I once did an experiment where the customer wanted to prune it but only a little which to be honest would of been a waste of time, it was way to big and needed taming, she was a bit nervous and anxious when I got those loppers out and reduced it from ten foot to two foot, those famous words, trust me I know what I am doing did nothing to ease her nervous disposition so after nearly four weeks plenty of new buds formed at six weeks lots of new foliage emerging at twelve weeks it was a lovely new Choysia and she thanked me and apologised for questioning my knowledge, that’s after eighteen years Working for her and knowing what I’m about, the Choysia was ternata Sundance and I did this in May of that year and with all renovation pruning I chucked plenty of buckets of water at it, thereafter it was kept small by selective pruning after flowering.