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The emergence of alternating twist multilayer graphene (ATMG) as ageneralization of twisted bilayer graphene (TBG) raises the question - in whatimportant ways do these systems differ? Here, we utilize ab-initio relaxationand single-particle theory, analytical strong coupling analysis, andHartree-Fock to contrast ATMG with $n=3,4,5,\ldots$ layers and TBG.$\textbf{I}$: We show how external fields enter in the decomposition of ATMGinto TBG and graphene subsystems. The parallel magnetic field has little effectfor $n$ odd due to mirror symmetry, but surprisingly also for any $n > 2$ if weare are the largest magic angle. $\textbf{II}$: We compute the relaxation ofthe multilayers leading to effective parameters for each TBG subsystem. We findthat the second magic angle for $n=5$, $\theta = 1.14$ is closest to the"chiral" model and thus may be an optimal host for fractional Chern insulators.$\textbf{III}$: We integrate out non-magic subsystems and reduce ATMG to itsmagic angle TBG subsystem with a screened interaction. $\textbf{IV}$: Weperform an analytic strong coupling analysis of the external fields andcorroborate it with Hartree-Fock. An in-plane magnetic field in TBG drives atransition to a valley Hall state or a gapless "magnetic semimetal." Adisplacement field $V$ has little effect on TBG, but induces a gapped phase inATMG for small $V$ for $n = 4$ and above a critical $V$ for $n = 3$. For $n\geq3$, we find the superexchange coupling - believed to set the scale ofsuperconductivity in the skyrmion mechanism - increases with $V$ at angles nearand below the magic angle. $\textbf{V}$: We complement our strong couplingapproach with a weak coupling theory of ATMG pair-breaking. While for $n=2$orbital effects of the in-plane magnetic field can give a critical field of thesame order as the Pauli field, for $n>2$ we expect the critical field to exceedthe Pauli limit.

TB or not TB? Contrasting properties of twisted bilayer graphene and the alternating twist $n$-layer structures ($n=3, 4, 5, \dots$)