  This contribution outlines the HALHF concept, which combines the high
gradients achievable in plasma-wakefield acceleration with conventional
radio-frequency acceleration. In HALHF, beam-driven plasma-wakefield cells are
used to accelerate electrons to high energy. Because plasma-based acceleration
of positrons is problematic, conventional RF acceleration is used but to much
lower energy. The HALHF concept utilises not only asymmetric energies but also
asymmetric bunch charges and asymmetric transverse emittances, leading to
comparable luminosity to conventional facilities but much lower capital cost.
Possible upgrades to the HALHF facility are discussed, in particular to the
$\rm{t\bar{t}}$ threshold and to 550 GeV, where the Higgs self-coupling and
$\rm{t\bar{t}}H$ coupling can be measured. Other upgrades include the provision
of two interaction points, to implement a $\gamma$$\unicode{x2013}$$\gamma$
collider of two possible types and finally a symmetric high-energy collider if
the problem of plasma-based positron acceleration can be solved.
