One of the things to appreciate about the original series of Doctor Who is that it had rules. Rules clearly laid down to define what Regeneration could and could not do, rules on what the Tardis could and could not do, and, over time rules to govern time-travelling.
Although the science governing time-travel was something that was only gradually developed, and was specifically the subject of 1972's Day of the Daleks, attitudes in the early years of the series tended to be governed by the fact that the Tardis was faulty and therefore never landed in the same time and place twice. So the question as to what might happen if the ship landed its crew in a time and place they were already existing in could be side-stepped... but What If....?
It's a question which might possibly be the subject of 1965s The Space Museum, a story which opens with the Tardis landing on a planet, next to a museum and the crew learning that they "..have jumped a time track" - their future selves are found as exhibits in the museum and destiny will see the watching phantom crew catch up with the 'present' and be forced to try and escape their fate.
It's a complex idea at work in this first episode, the suggestion is the Tardis has malfunctioned perhaps and delivered its crew into their near future, a future that saw them captured and turned into grotesque exhibits behind glass cases. As time catches up and the crew slip into phase the exhibits disappear and they enter the present. Can they avoid their fate?
More to the point though this is a unique example of Time-travel itself being used and studied in the series' earliest years, and forms a part of the insight into what the producer and writers attitudes to the science of it might have been at the time.
Is it possible for the same person to exist simultaneously with themselves is the question. And the answer seems to suggest that the makers of Doctor Who at this time considered the answer as "No".
If natural safety devices in both the Tardis and time itself act to keep the crew from ever sharing the same time and place it can never happen, but if something went wrong... and it DID happen, then the view at this time in the series' history is that the 'visiting' time-traveller would become a phantom, out of phase with reality, and could only be a spectator on the present and their 'future' selves. It's a concept that echoes the science seen in Superman comics of the sixties up till the mid-eighties. A sixties view on the science that would govern time-travel... and in principle the concept is a sound one. For some reason however the neatness of this concept of a safety-valve that shifts a visiting time-traveller into a phantom state that is out of phase with their environment is something that fiction phased out of its literature. Why.... is hard to say. As it IS a very neat and practical idea to rationalise the science that would have to underpin time-travel. (Coffee)
In the Justice League Cartoon, Superman got blasted into the far future and was thought to be dead.
He meets Vandal Savage and they finish his time machine but VS states he cannot travel back to an era where he already exists. But he can send Superman back home to prevent that dark future from occurring.
In the early Fantastic Four and Avengers it was shown that Doom's time machine which Reed later takes as his own can send someone back and keep them out of phase so that they can observe without interfering....except for the time when Cap travels back to see if Bucky did survive and the machine was adjusted to allow Cap to materialize and fight in the past to ensure his past self was thrown into the ice....
So at some point there was indeed a firm rule that the past cannot be altered, only fulfilled and that someone cannot/should not exist in an era that they are already in.