So far as I know, there is no limit, except that the person must be qualified in each case.
The clearest qualification is from being an elector in the parish. In some situations (for example, a student) it is possible to be on more than one electoral register.
Other qualifications can be selected from:
For the whole of the 12 months until nomination, the person has occupied land or other premises in the parish (as owner or tenant)
Has resided in the parish or within 3 miles for the same period. Residence requires having somewhere to sleep, but a person can have more than one residence.
Has had a principal or only place of work in the parish for the same period. Being a councillor counts as working in the parish, so will qualify a person to stand for re-election. But the workplace qualification can only be used in a single parish because of the words "principal or only".
This all assumes the person qualifies in relation to age and citizenship.
Beyond all this, it is up to the electors, if there are enough candidates!