Weeds to introduce into lawn that is mown regularly.

I'm looking for good weeds to introduce into my lawn. It is not a meadow, so they should be able to survive regular mowing, and ideally not be thugs that will destroy a border if they get into it. Right now I have a lot of white clover and daisies; I am introducing self-heal and yarrow and was considering creeping cinquefoil, but fear it may be too thuggish. The clover works really well, as it is very drought resistant and keeps the lawn greener for much longer., and the daisies are just a joy. I have two patches that are allowed to flower, so these are not mown during summer and allow the clover and anything else in there to self-seed. Another consideration is that the weeds or plants should combine well with grass; I have bits where acaena and thyme romp into the lawn, which is lovely, but on a larger scale I think that something like a camomile/thyme/acaena etc lawn will require weeding out of grass, which is not my intention.
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I tend to leave most wild flowers in my lawn apart from one's that have leaves flat to the ground as they stop anything else from growing. I've never actually planted anything in my lawn, - even grass! I just wait to see what pops up.