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There were countless billions of dimensions, some of them incomprehensibly different to N-Space. Beings from these distant dimensions obeyed very different laws of physics and were (presumably) forbidden to cross into other dimensions. Nobody No-One came from a reality 45 billion dimensions away from N-Space and was composed of language and communication instead of matter and energy. (AUDIO: The Word Lord)
The Sixth Doctor described there being trillions and trillions of alternate dimensions, some of which could be infinitesimally small micro-universes. (AUDIO: The Macros) However, the Seventh Doctor later commented that one billion cubic centimetres was small in terms of a dimension's size. (AUDIO: The Light at the End)
Time was often considered by humans to be the "fourth dimension" (TV: "An Unearthly Child") and Vicki Pallister later elaborated that time, even though a dimension in itself, had dimensions of its own. The First Doctor even stated, in their adventure at the time, that he did not understand "this" fourth dimension. (TV: The Space Museum) Different universes possessed different time dimensions. Time moved faster in Capron's universe, requiring metabolisms to be altered so as to prevent rapid ageing when travelling to it from N-space. (AUDIO: The Macros)
According to the Twelfth Doctor, the Boneless were "from a universe with only two dimensions", although the Doctor also described them as "creatures from another dimension" and mentioned a way of sending them "back to their own dimension". People in N-Space, where three dimensions were required for life to survive there, had theorised such a universe's existence, but according to the Doctor, "no-one could go there and prove its existence without a heck of a diet". (TV: Flatline)