Can't seem to add custom fields to the sublist on assembly build records, is it impossible?

@Axel Create a transaction body field. Select "work order/assembly builds" under the subtab "applies to". Then press "save and apply to forms" and select the proper form you want it to be populated in.

Thanks for your reply, but I want a Line field, which seems impossible

Create a transaction line and check "applies to work order". You can then apply it to assembly builds too.

Support confirmed that it is not possible through basic customization.. "Upon further reviewing, the ability to add a Custom Transaction Line field on the Assembly Build page through basic customization is still being filed as an enhancement."