Is it possible to master two different typing keyboard layouts? I am a good typist with qwerty keyboard, I came across other keyboard layouts (eg: Dvorak keyboard). I believe I will never be able to master these two typing layouts simultaneously.

Am I right? or is it possible to learn both and become a good typist (i.e type with decent speed without looking the keyboard).

The example in itself is trivial to me (I am happy with qwerty keyboards) but I wanted to understand what will happen when there is a serious overlap and contradiction with two methods and can human mind handle it or is it once set it's really set in situations like this?

If my mind can learn only one method when two contradicting and interfering methods are present, then I believe it's implications are very interesting.

There are real life examples which are similar to the keyboard example.
They all have the following attributes.
a) Two are more conflicting solutions for same problem
b) Decisions must be automatic or made under tight time constraint (no time to think).
Observational points:
It would be straightforward to point to a person who has mastered more than one keyboard layout (e.g., some of the people here). So, yes, it is possible. From my own personal experience, I can point to my use of both Vim keyboard shortcuts for editing and regular OSX/Windows keyboard shortcuts. This is certainly possible. 

But I'd prefer to focus on the scientific principles that underly such a capacity.

Scientific principles:

There are a number of scientific principles operating in this context.


Negative and positive transfer
Principles of task consistency and complexity


In general transfer of skill from one domain to another depends on the degree of consistency between the two skills. This is a broad concept. Certainly the mapping between inputs and outputs is a big part of this (i.e., key press and letter). But it could also include a range of broader conceptual and psychomotor routines.
Thus, positive transfer occurs when you can take the skill on one task to improve your performance in another. Negative transfer occurs when your performance on one task suffers as a result of learning a different task. In general positive transfer is much more powerful than negative transfer. 

Applying these principles to converting from QWERTY to DVORAK

Let's say that you have a person who has learnt the QWERTY keyboard layout and can type 80 words per minute. They decide that they want to learn DVORAK. What would we expect from a skill acquisition perspective?

The new keyboard layout (DVORAK) shares many consistent cognitive and psychomotor elements with the original layout (QWERTY). The basic motor actions of pressing individual keys are identical. Many other cognitive skills around the concept of typing are also the same. However, the actual specific key-to-letter mappings will be new. Furthermore, learning to type involves building up specific motor patterns around common sequences of letters and some of these will also be new. 

The net result will be that learning to efficiently use DVORAK should take a fair bit of time. However, the learning curve should be massively faster than learning how to touch type the first time. Thus, in a basic sense, the main limitation to learning to type using two keyboard layouts is that it just takes more time than to learn one layout. And generally, you will be better at one layout than the other, so why bother learning two layouts unless perhaps you are transitioning to a new layout for the long term.

Based on general principles of cognitive transfer, generally knowing QWERTY will make DVORAK easier to learn. So most of the transfer will be positive. It is likely that there will be some accidental applications of QWERTY when you are in DVORAK and vice versa. Such errors can be minimised if you can create stimuli in your task environment that clearly communicates the appropriate mapping (e.g., use it on particular computers). The general concept in skill acquisition is that a single stimulus-response pairing is easier to manage, but over time you will learn to apply contextual cues to choose the correct stimulus-response options.

Another general principle for psychomotor skills is that forgetting is slower and relearning is quicker than for a lot of cognitive skills (Rosenbaum et al, 2001). Thus, people are likely to be able to retain and get back up to speed on a previously learnt keyboard layout after a period of using a newer layout.

References

If you're interested in reading more, you might want to check out some of Philip Ackerman's early work on skill acquisition where he talks about consistency and complexity.

There's also a large literature that has studied the cognitive psychology of learning to touch type.


Ackerman, P. L. (1989). Within-task intercorrelations of skilled performance: Implications for predicting individual differences? A comment on Henry &amp; Hulin, 1987.
Ackerman, P. L. (1988). Determinants of individual differences during skill acquisition: cognitive abilities and information processing. Journal of experimental psychology: General, 117(3), 288.
Rosenbaum, D. A., Carlson, R. A., &amp; Gilmore, R. O. (2001). Acquisition of intellectual and perceptual-motor skills. Annual review of psychology, 52(1), 453-470.
Yechiam, E., Erev, I., Yehene, V., and Gopher, D. (2004). Melioration and the transition from touch-typing training to everyday use. Human Factors, 45, 671-684.