EBM and Arc are the main method to melt down high melting-point metals. Induction is possible too, although to the border line (people use VIM to melt Ti alloy). The biggest concern is the crucible reactions. Ti is very reactive, it will react with almost any ceramic crucbile (Al, Si Zr,Ca oxides. oxygen control is a big deal.
Graphite maybe a choice. Often, people use crucible less melting (e.g. water-cooled cu crucible) to prevent crucible contamination.