Just like anything else that gets planted in the garden, new perennials seem to be so cute and innocent. They get even better as they mature. Some grow and spread to impressive proportions. Then . . . some perennials get to be too large. Some get overgrown enough to obscure their own appealing characteristics or other plants. Others get crowded enough to inhibit their own bloom.
Lily of the Nile, which is one of the most common and resilient of perennials, grows and blooms indefinitely. It does not spread too quickly, but eventually creeps a few feet every decade or so. However, if it is too healthy, individual shoots can get too crowded to bloom as prolifically as they want to. Also, shoots that get too close to walkways or other plants eventually become obtrusive.
Anyone who has tried to shear encroaching foliage of lily of the Nile knows that doing so ruins the natural lushness of the foliage. Once scalped, it will stay that way until obscured by new foliage that will be just as obtrusive as the removed foliage. The only remedy is to remove the shoots that produce the foliage, leaving the shoots behind them with adequate clearance for their foliage.
Lily of the Nile shoots are not easy to remove. Their rubbery roots have quite a grip! Yet, once removed, the stout stems can be planted as new plants wherever more new plants are desired. They only need to be watered regularly for the first few months until winter, so that they can disperse roots. If dug and replanted in autumn, they generate roots over winter, and are ready to go by spring.
Overly congested colonies of lily of the Nile, as well as African iris and New Zealand flax, can be dug, split into individual shoots, groomed of deteriorating foliage, and then replanted. Because New Zealand flax has such big leaves, it should be processed in autumn or winter; and its leaves should be cut short so that they do not get tattered and floppy while new foliage and shoots grow.
Bird of Paradise can be divided similarly, but carefully because the shoots are surprisingly fragile. However, giant bird of Paradise is a completely different animal. The tallest trunks eventually begin to deteriorate, so get cut down like trees. Basal shoots are left intact to replace them, so only get divided if obtrusive or overly abundant. Most perennials prefer to be divided after bloom.
Canna and calla prefer to be dug and relocated as their foliage dies back after bloom, just before new shoots develop. However, new shoots often develop before older foliage must be cut back.
Tony Tomeo 
I have had cannas that have gotten out of control. They are definitely hard to dig and kill.
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Kill?! That makes them sound so undesirable. I suppose I would dislike them if they grew like weeds like they do in other climates. They do not get very far here because they want more water that what they get.
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They do grow like weeds here. The ones that go out of bounds were passalongs. Should have know better.
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I keep planting those that get divided. They still seem so innocent. There is the possibility that once they get dispersed out into all the landscapes, that they could start growing like weeds all at the same time!
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I used to be the gardener for my church grounds, and on one patio area were three large pots planted in New Zealand flax. They had to be watered with a hose, and though they were wonderfully drought tolerant, I did manage to kill one by neglecting to water it.
I searched the whole county in vain for another plant of that species before I came up with the brilliant idea to divide the two living plants and put half of each into the empty pot. That way the two old plants also got refreshed by being thinned out and getting new potting soil. It was an hours-long project dealing with the heavy pots and the thick roots, but fun and satisfying.
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BINGO! They do appreciate getting divided every once in a while, especially if potted. In the future, you will likely want to divide them again, even if there is no use for the pups. At the Felton Presbyterian Church, we planted many lily-of-the-Nile that needed to be removed from a home in Capitola. (Unfortunately, many were discarded shortly afterward to make room for an unmaintained rose garden.
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None of these plants are in my garden, but the principle of overgrown perennials still applies. For me it has happened most frequently with Daylilies and grasses like Switchgrass and Sea Oats.
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Yup. I probably should have mentioned daylilies, but did not think of them because they do not grow quite as vigorously as they do in other regions. Do you happen to have cannas in your garden? I can not remember. I was VERY surprised to see the in Oklahoma.
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