Einstein & followers proved GR(Λ) – general relativity with cosmical constant Λ – is the unique gravity theory obeying certain postulates. We show a loophole: allowing traceless Lanczos tensors _abc permits more theories. That's desirable because GR contradicts observation – with two proposed remedies:

DM: copious invisible "dark matter"(≈5× "normal matter" mass, and distributed differently) exists;
MOND: replace GR by Milgrom's "modified Newtonian dynamics."

But: most experts claim DM has never been detected; MOND fits many observations better; and allowing any undetectable-DM distribution makes DM largely uncheckable/unusable. Meanwhile, MOND is theoretically unacceptable: not "generally covariant," with relativistic-MOND attempts ugly, complicated,highly non-unique, asininely demanding new fields ("dark matter" rematerializes!), and often afflicted with tachyons/acausality/instability.

We propose new simple "Switcheroo" (SG) and "Lanczos Gravity" (LG). Redone uniqueness arguments suggest LG/SG are the only theoretically-acceptable GR(Λ) extensions. LG uses L_abc and/or its "superpotential" P_ab to modify Einstein's field equation. SG obeys the unmodified equation, except Λ "switches" among multiple possible values, presumably from different quantum field (QF) vacuum phases in different places. Λ-stairstep phase-transitions ("switcheroos") occur when certain tensorial-invariant scalars F⃗ cross certain boundaries. The formulas for F⃗, while not entirely known, importantly involve L_abcL^abcand/or L*_abcL^abc (* means tensor dual). Remarkably, {L_abc, P_ab} exists only in 4 spacetime dimensions. Gravitationally L_abc looks analogous to the "4-potential" vector A^u in electromagnetism. In QF theories A^u is central while electric/magnetic fields are not; so analogously L_abc might underpin future "quantum gravity" theories, not Weyl's curvature tensor W^a_bcd.GR can be reformulated based on Ricci curvature R_ab and {L_abc or P_ab}, rather than the metric g_ab. One should a priori expect switcheroos given no known reason for QF vacuum phase uniqueness yielding one Λ value always. For MOND-like SG behavior, F⃗ must involve L_abc because invariants involving only the metric tensor and its derivatives cannot work.

LG/SG contain GR, hence fit observations no worse. LG/SG potentially could explain: galaxy rotation curves, early big bang "inflation," recently-alleged nonconstancy of Λ during cosmological (FLRW model) history, "Hubble tension," and solve:galaxy-formation puzzles, "lithium problem," "satellite problem," black hole paradoxes, and perhaps "defend" against singularities. I do not know whether SG/LG really accomplish that, or are garbage. Answering that question could be long and difficult for astronomers. Complications: LG/SG and DM could coexist; it's unclear how SG/LG should best-handle Lanczos nonuniqueness; and the full set of possible LG gravity theories remain unclassified.