The main options (as far as my limited knowledge goes) seem to be:
16,000t - LPD (R) Albion Class Landing Platform Dock, United Kingdom
16,200t - Bay Class Auxiliary Ship Alternative Landing Ship Logistic (ALSL), United Kingdom
13,900t/12,750t-16,800t Galicia/Rotterdam Class Landing Platform Docks (LPD), Spain/Netherlands
12,000t LSD Foudre Class Landing Platform Docks, France
enlarged version of 9,000t MRV Canterbury, Netherlands/Australia
or the JHSV Fast Catamaran Transport Program.
Albion is over 18000 tons full load, but as StevoJH says, too expensive for the role.
Bay/Galicia/Rotterdam/De Witt are variants of the same basic
Schelde Enforcer design. A basic, stripped-down model could do the job & might be within budget. There are also smaller versions, & I think one was offered to the RNZN, but it bought
Canterbury. Navantia can build it.
The
Foudre class is no longer offered, AFAIK, though they might dust off the blueprints if asked. Huge dock, but correspondingly limited lane-metres, I think. Depends on what the requirement is.
Fincantieri & TKMS also offer ships. Fincantieri has
LPD/LHD designs, & TKMS has the
MESHD or MHD dock/support ship, configurable for RAS, a transport which does not need a port, or as an LHD. Fincantieri also does replenishment ships, of course.
Flensburg have a couple of
sealift & sealift-cum-replenishment ships - not only the Point-class.
And for the wild card, there's always the Korean option. Indonesia has a few very cheap Korean LPDs of ca 11000 tons (
Makassar class), built to merchant standards, by a commercial yard. If the requirement is for an austere ship, a transport with a dock rather than a true amphibious assault ship, I think it would be well worth examining that option.