Do you think various forms of punishment can be done in conjunction with one another or should they be independent of one another?
It would be helpful to know what type of punishment(s) you are referring to.
It is not unusual for a conviction for a crime to include more than one form of penalty to be served or performed at the same time. Persons convicted of traffic violations, for example, may have to pay a fine in addition to having a restriction placed on their driving authorization or being required to complete a course of drivers' training classes. Persons may be responsible for doing community service work for a given period of time in addition to paying a fine or reporting to a parole officer periodically.
For persons commiting more serious offenses, it is not unusual for the judgement to set multiple prison terms to be served simultaneously - at the same time.