  The measurement of the triple Higgs coupling is one of the main tasks of the
(HL-)LHC and future lepton colliders. Similarly, triple Higgs couplings
involving BSM Higgs bosons are of high interest. Within the framework of Two
Higgs Doublet Models (2HDM) we investigate the allowed ranges for all triple
Higgs couplings involving at least one light, SM-like Higgs boson. We present
newly the allowed ranges for 2HDM type III and IV and update the results within
the type I and II. We take into account theoretical constraints from unitarity
and stability, experimental constraints from direct BSM Higgs-boson searches,
measurements of the rates of the SM-like Higgs-boson at the LHC, as well as
flavor observables and electroweak precision data. For the SM-type triple Higgs
coupling w.r.t. its SM value, $\lambda_{hhh}/\lambda_{hhh}^\mathrm{SM}$, we
find allowed intervals of $\sim [-0.5,1.3]$ in type~I and $\sim [0.5,1.0]$ in
the other Yukawa types. These allowed ranges have important implications for
the experimental determination of this coupling at future collider experiments.
We find the coupling $\lambda_{hhH}$ between $\sim -1.5$ and $\sim +1.5$ in the
four Yukawa types. For the triple Higgs couplings involving two heavy neutral
Higgs bosons, $\lambda_{hHH}$ and $\lambda_{hAA}$ we find values between $\sim
-0.5$ and $\sim 16$, and between $\sim -1$ and $\sim 32$ for
$\lambda_{hH^+H^-}$. These potentially large values could lead to strongly
enhanced production of two Higgs-bosons at the HL-LHC or high-energy lepton
colliders.
