It would be quite straightforward to incorporate Jackendoff's theory of conceptual structures into a typed feature-based grammatical framework like HPSG. Some notions within Jackendoff's theory transfer almost directly to HPSG, and many of the notational and operational details of the theory are actually captured more consistently within HPSG. We discuss how below.
The core of Jackendoff's theory consists of the semantic ontology and the definition of function-argument structures in terms of elements in this ontology. This corresponds directly to the notion of type constraints on the structure of signs in HPSG. The ontology would be defined within the sort hierarchy, anchored at the content sort. Each function-argument structure can be defined as a feature structure of a particular subtype of qfpsoa whose arguments are restricted to be of a particular type. Words functioning as lexical heads would be given a semantic specification in their lexical entries corresponding to one of the ontological types; in particular, verb meanings would be decomposed into a function-argument structure for either an Event or State.
Jackendoff has argued that a single entity may correspond to multiple semantic roles within a relation. This can be easily modeled in HPSG with structure-sharing between the values of each semantic role which the entity fills and the index of the entity. Any type constraints (i.e. both of ontological category and more specific selectional restrictions) imposed on a subcategorised argument can be enforced through required type compatibility during unification. No special operation needs to be defined to handle this, assuming that the sort hierarchy has been adequately defined. The use of HPSG to handle this mechanism has an additional benefit: HPSG makes explicit the existence of a hierarchy which Jackendoff implicitly assumes. A semantic hierarchy is fundamental to HPSG and therefore the notion of ``compatibility'' between entities on which Jackendoff depends can be handled directly.
To generalise over the semantic contribution certain adjuncts make,
Jackendoff introduces adjunct rules which specify how the
semantics of an adjunct is to be combined with the semantics of the
verb phrase it modifies. These rules specify both the syntactic and
semantic structure of the verb phrase which a particular adjunct can
modify. The actual combination of the semantics of the VP and the
adjunct is accomplished via an adjunct fusion rule. This rule is
essentially analogous to the function the Head-Adjunct schema
performs in HPSG, while the details of particular adjunct rules can be
captured in the signs for each adjunct, in the
synsem 
local category head mod and the
content features. Thus the mechanisms required for
Jackendoff's theory already exist within HPSG.