Hi, Graham
All TPC widgets are configured to allow for most of Dynamic CRM features which includes multiselect picklist. If the picklist is configured that way in the CRM, when you select the attribute on the TPC Portal and click the Appearance tab, you will see the option for selecting multi-select (which should be default).
Lookups cannot be configured this way. However, you can present one to many relationships using a
TPC Sub-grid e.g., (a contact can have many related cases).