Select the most appropriate adjective to fill in the blank. Do you have any…

The words 'far,' 'further,' 'farther,' 'furthest,' and 'farthest' form two related comparison chains, but the two chains are not symmetric. 'Farther' and 'farthest' are restricted in standard usage to measurable physical distance only. 'Further' and 'furthest' are general-purpose forms: they are the standard choice for abstract, non-physical extent -- additional degree, quantity, time, or scope -- and, per many usage guides, they are also acceptable for physical distance, unlike 'farther/farthest,' which cannot describe abstract extent.

In this sentence, the blank modifies 'plans' -- an abstract noun (a course of action), not a physical location or measurable distance. Since 'farther' and 'farthest' are restricted to physical distance, both are ruled out here. Between the two general-purpose forms, the sentence asks whether the person has any additional plans -- a general comparative sense of 'more' or 'additional,' not a request for the single most extreme or final plan. The comparative form correctly conveys 'any additional plans,' while the superlative form would instead ask for the single furthest-reaching plan.

Contrasting each option by value confirms this:

• further -- comparative, general-purpose (abstract extent, and per usage guides also physical distance), e.g., 'further discussion.'

• farther -- comparative, restricted to physical distance only, e.g., 'farther down the road.'

• farthest -- superlative, restricted to physical distance only, e.g., 'the farthest planet from the sun.'

• furthest -- superlative, general-purpose (abstract extent, and per usage guides also physical distance), e.g., 'the furthest extent of his research.'

Because 'plans' is abstract -- which rules out the physical-distance-only forms -- and the sentence calls for a general comparative sense of 'more/additional' rather than an extreme superlative, the general-purpose comparative form is the grammatically correct choice here. The correct adjective is 'further.'