If a speedlight isn't enough, chances are good you'll have to move up to more expensive, bigger flashes, which in turn may require bigger, sturdier support gear and modifiers. Most folks would typically recommend a studio strobe, and if you're on a budget and in the United States, one good option are the Paul C. Buff lights, such as the Alien Bees or Einsteins. Another option is to get cheap Chinese-manufactured strobes off eBay/Amazon whatever, but the quality and light output of these varies.

Another option would be to look at the Godox "bare bulb" battery-powered Witstro flashes. These are rebranded under a number of names, such as Adorama's Flashpoint Streaklight and Flashpoint eVOLV. They're roughly the equivalent of ganging two or three speedlights together, and they have bare bulbs, which spread out the light in a pattern that's similar to a studio strobe, and which can fill modifiers like softboxes better. The upcoming AD200 (aka the Flashpoint eVOLV at Adorama) is the same size as a speedlight.

Also, both the AD360II and the AD200 have built-in receivers that can be used with an X1T-S transmitter to enable HSS and TTL from a Sony camera with a multi-interface hotshoe. You may be able to get it to work with an α900 with an ADP-AMA hotshoe adapter.