The GDPR says that you can assign further tasks and duties, so long as they don´t result in a conflict of interests with the DPO´s primary tasks.
As an example of assigning other tasks, Article 30 requires that organisations must maintain records of processing operations. There is nothing preventing this task being allocated to the DPO.
Basically this means the DPO cannot hold a position within your organisation that leads him or her to determine the purposes and the means of the processing of personal data. At the same time, the DPO shouldn´t be expected to manage competing objectives that could result in data protection taking a secondary role to business interests.
A company´s head of marketing plans an advertising campaign, including which of the company´s customers to target, what method of communication and the personal details to use. This person cannot also be the company´s DPO, as the decision-making is likely to lead to a conflict of interests between the campaign´s aims and the company´s data protection obligations.
On the other hand, a public authority could appoint its existing FOI officer / records manager as its DPO. There is no conflict of interests here as these roles are about ensuring information rights compliance, rather than making decisions about the purposes of processing.