  In this work, we analyze the asymptotic behaviors of high-order rogue wave
solutions with multiple large parameters and discover novel rogue wave
patterns, including claw-like, OTR-type, TTR-type, semi-modified TTR-type, and
their modified patterns. A correlation is established between these rogue wave
patterns and the root structures of the Adler--Moser polynomials with multiple
roots. At the positions in the $(x,t)$-plane corresponding to single roots of
the Adler--Moser polynomials, these high-order rogue wave patterns
asymptotically approach first-order rogue waves. At the positions in the
$(x,t)$-plane corresponding to multiple roots of the Adler--Moser polynomials,
these rogue wave patterns asymptotically tend toward lower-order fundamental
rogue waves, dispersed first-order rogue waves, or mixed structures of these
rogue waves. These structures are related to the root structures of special
Adler--Moser polynomials with new free parameters, such as the
Yablonskii--Vorob'ev polynomial hierarchy, among others. Notably, the positions
of the fundamental lower-order rogue waves or mixed structures in these rogue
wave patterns can be controlled freely under specific conditions.
