Run Alpine on very Thin Client

What I am trying to do is run recent Alpine on Fujitsu Futro S300 Thin Client with 256 MB of RAM. The root filesystem's capacity is insufficient to accommodate all services (only 115 MB), so I need to know if there is a way to influence root tmpfs size, or do I have to look for a 512 MB SDRAM SODIMM module which is practically very rare.
Thank in advance for tips.
Maciej