Tim Bowen has come up with the perfect description of the phrasal verbs associated with this word.

In a study published in the UK, fast food, and in particular junk food aimed at children, came in for (received or attracted) a lot of criticism. As a result, some food companies began to come round (change their opinion in the face of persuasion) and tried to come up with (think of) ways of reducing the sugar and salt contents in their products without affecting the flavour. Previous campaigns to encourage consumers to eat healthier foods have sometimes come up against (met with) opposition and such efforts have rarely come off (succeeded).

The issue seems to come down to (be centred on) the question of personal choice and although official figures show that obesity, and particularly childhood obesity, is a problem that is becoming more acute, there is some disagreement about exactly how the current situation has come about (happened). Some people come at (approach) the problem from a different angle, suggesting that it is a matter of exercise, not diet. They argue that if people exercise regularly, they are less likely to come down with (become ill with) certain diseases. Some experts have come out in favour of (publicly stated their support for) an official advertising campaign promoting the benefits of exercise and a healthy diet. Others remain sceptical, claiming that such campaigns do not come under (are not the responsibility of) the government’s remit and that it is up to people to make their own choices. One thing is certain, however: too much sugar makes you come out in spots.