It depends on how sophisticated the boiler mfr is. Several things would change , besides the wall thickness of pressure parts, including:
a) the steam outlet enthalpy changes, so the boiler firing rate must change. This affects fan size , burner size, emmissions permits, etc.
b)The sizing of the steanm drum driers and seperators may need to change, based on the changed specific volume of steam ( driers) and 2-phase flow (seperators). For large natural circulation boilers, the drum sizing is usually dictated by the length and dia. needed to contain these driers and seperators.
c)To prevent dryout and DNB in the waterwall tubes, the waterwall circulation system is designed to ensure an adequate circulation ratio is provided. This involves the sizing of the downcomers, inlet feeders, inlet headers, watewall tube size, outlet header and unheated outlet risers, the distribution of these risers to sections of seperators and segmenting of headers. This calculation is dependent on the specific volume of steam, as well as the distribution of radiant heat absorption in the furnace. The higher pressrue leads to a smaller steam specific volume and a reduced driving force for natural circulation.
d) Above certain pressures, there is usually mandated a change to the range of permitted feedwater treatment methods and water quality, espescially if the boiler is feeding a steam turbine.