Yes, there are some oddball baryons that contain four quarks and one anti-quark. They're called pentaquarks. These could be thought of as a baryon with three quarks plus a meson with a quark anti-quark pair, but sticking to each other more than they should. There are few hadrons that survive more than a tiny fraction of a second, and only the proton and neutron live longer than one second. The "sticky" baryon-meson combinations are found through analysis of scattering data at the major particle accelerators.
The known pentaquarks are: $P_c(4450)^+$, $P_c(4380)^+$ ([CERN 2015], [Arxiv paper]) and $P_c(4312)^+$ ([CERN 2019]) - oh but wait, the 4450 one seems to really be two pentquark peaks close together in mass - 4440 and 4457.[CERN] BTW, the subscript 'c' indicates that one of the constituent quarks is a c (charmed) quark.
There's a tetraquark - two quarks and two anti-quarks in one bag - with mass 4430, named $Z(4430)^+$ (nothing to do with the Z boson). [CERN] Can it be described as two mesons being "sticky" with each other or is it better described as a more tightly-knit group of four of the little buggers?
Another possible exotic hadron is made of six quarks all stuck together. This is a "dibaryon". When I was an undergrad in physics, I worked with Dr. Yokosawa at Argonne National Laboratory on finding bumps in polarized proton-proton scattering. That was an interesting experience. As of last time I checked the literature, there was [only one found] that stood up to analysis, but always there are candidates due to unexplained wiggles in cross-section vs energy plots. These usually turn out to be something less exotic. Interesting, but since anti-quarks aren't involved, never mind!
: https://home.cern/news/press-release/cern/cerns-lhcb-experiment-reports-observation-exotic-pentaquark-particles CERN’s LHCb experiment reports observation of exotic pentaquark particles (14 JULY, 2015)
: https://arxiv.org/abs/1507.03414 Observation of J/ψp resonances consistent with pentaquark states in Λ0b→J/ψK−p decays (LHCb collaboration)
: https://home.cern/news/news/physics/lhcb-experiment-discovers-new-pentaquark LHCb experiment discovers a new pentaquark
: http://lhcb-public.web.cern.ch/lhcb-public/Welcome.html#Pentaq 26 March 2019: Observation of new pentaquarks
: http://lhcb-public.web.cern.ch/lhcb-public/Welcome.html#Z%284430%29 9 April 2014: Unambiguous observation of an exotic particle which cannot be classified within the traditional quark model.
: https://arxiv.org/abs/1610.05591 On the History of Dibaryons and their Final Observation, H. Clement