Other colours that work with red are turquoise, apricot, peach, any blues, yellow, even some pinks and greens. (Look to gardens for inspiration, or Old Masters paintings). I'd find patterns with combinations of those, or Vys colours, in a rug, and chairs or cushions.

A mixture of bold vibrants colours are my forecast for 2016. Its all about contrast!

Teal works really well with dark chocolate brown and beige (greeny blue teals with deep brown leather sofas or tables and caramel walls pop and yet are homely and comfortable) so a rug underneath the table and sofa to delineate that space with teal in it or all teal (I would go for a pattern as you have very neutral pieces the one from Kathy above with caramel and beige is perfect I think) could work -ditto curtains and cushions. Given the neutral pieces you could add pops of another colour depending on the teal tones you use. Also lighter turquoise tones that sort of layer with teal - its deeper cousin.... a turquoise ceramic (or other objects) with a toning teal one ( teal and turquoise can vary on the blue-green spectrum) and a lovely caramel coloured piece ( things work well together in 3's I find) all of varying heights shapes and some texture on at least 1 - would look great somewhere. Burnt orange (a more subtle tone than hot orange) can be a great and more adventurous addition as can khaki - just keep them subtle and mix it up. I have a great market bought cushion made from an old woollen tartan type blanket of aqua /turquoise, a light khaki and burnt orange with a caramel leather cross on it that looks so good on my dark brown leather sofa (sorry no photo on me).

printed brownish one is for master bedroom and living, kitchen and dining.its blockout snd see through. marble - white one block out is for all other bedrooms