Improved limits on $\beta^-$ and $\beta^-\beta^-$ decays of $^{48}$Ca

New limits on $^{48}$Ca $\beta^-$ and $\beta^-\beta^-$ decays to excited states of $^{48}$Ti have been obtained using a 400 cm$^3$ low-background HPGe detector and an external source of 24.558 g enriched CaF$_2$ powder (9.822 g of $^{48}$Ca). The limits for $\beta^-$ decay to the $6^+$ ground state, excited $5^+$ and $4^+$ states in $^{48}$Sc are $1.6\cdot 10^{20}$ yr, $2.5\cdot 10^{20}$ yr, and $1.9\cdot 10^{20}$ yr at the 90% confidence level. For the $\beta^-\beta^-$ decay to $^{48}$Ti the limits to the first $2^+$, second $2^+$ and first $0^+$ excited states are $1.8\cdot 10^{20}$ yr, $1.5\cdot 10^{20}$ yr, and $1.5\cdot 10^{20}$ yr again at the 90% confidence level.