The assumption that heads always share their logical form with the mother node will be too restrictive for several linguistic or semantic theories. Some extensions to BUG1 are possible that handle more sophisticated grammars. For example it is possible, as proposed in , to enlarge the power of the prediction step. By inspection of the grammar it may be possible to precompile possible relations between the logical form of some top node and the logical form of the pivot of that node.
Another extension is the architecture advocated in , where rules are divided into two types. The first type of rules are the ones where the head indeed shares its logical form with the mother node. In the second type of rule there is no such node. The algorithm does not necessarily predict a lexical entry, but it predicts a rule of the second type, or a lexical entry. The daughters of this rule are then generated in a top-down fashion after which the mother node of the rule is connected to the top node bottom-up, as in BUG1. In case all rules of a grammar are of the first type the algorithm behaves similar to BUG1. In case no rules have a head, the algorithm reduces to a top-down generator.
In the generator for UCG  it is also assumed that heads share their logical form with the mother node (`all logical forms are projected from the lexicon'); as an extension to this, a special arrangement is made to allow for typeraising as well.