Summary
Not all sequences with improved activity have plausible evolutionary paths via stepwise introduction of mutations (1–2). One report found that a protein’s ancestry limits the range of high-fitness sequences that can be explored (4). This suggests that engineered libraries can access mutation combinations that are inaccessible to stepwise methods. Experimental evidence contradicting this claim also exists (5) (Fitness landscapes are locally smooth but globally rugged). Kirby et al found evidence against this in antibodies (6).
Details
In (1), the phosphotriesterase design PTE_5 differs from dPTE2 by four mutations that were inserted simultaneously, but does not have a plausible evolutionary path to high fitness.
In (2), where a library of 160,000 sequences saturating four positions of TrpB (tryptophan synthase) was generated, 20% of starting points had no plausible path to the optimal sequence.
(3) found that adenylate kinase variants using either zinc of hydrogen-bond networks could not be traverse by individual point mutations.
Figures

Ref (2)

Ref (3)
(4)