The conditions can be combined, if the manifestations are duplicative and overlapping. This is often not the case however.
Here is the verbiage from a successful appeal.
The RO found that 38 C.F.R. § 4.96 bars the assignment of a
separate rating for the asthma condition apart from the sleep
apnea condition. However, that provision states that ratings
under Diagnostic Codes 6600 through 6817 will not be combined
with each other. That provision also states that ratings
under Diagnostic Codes 6822 through 6847 will not be combined
with each other. The two specified ranges of diagnostic
codes are stated in the disjunctive and thus, the provision
does not automatically prohibit the assignment of a rating
under Diagnostic Codes 6600 through 6604 in addition to the
assignment of a rating under Diagnostic Codes 6822 through
6847.
Furthermore, under 38 C.F.R. § 4.96, a separate rating can be
assigned for asthma even when the veteran is receiving
compensation for sleep apnea. While these respiratory
conditions each impair his ability to breathe, each condition
has distinct and separate symptomatology. The sleep apnea is
caused by obstructive factors and results in disruption of
breathing during sleep; the condition is alleviated by the
use of CPAP. The asthma is caused by exposure to allergens
and irritant particles and results in recurrent attacks of
spasmodic contraction of the bronchi; the condition is
alleviated by the use of bronchodilators. Because the
symptomatology does not overlap, a separate rating should be
assigned for the asthma. See Esteban v. Brown, 6 Vet. App.
259, 261-62 (1994).
