It is not uncommon for more then one Martial Art to interest a potential
student.  The logical question is, "Can I" or "Should I study them both?"

This is a matter of some debate and opinions differ.  The prevailing wisdom is
a bit of a compromise.  It is generally recommended not to study more then one
art at a time or, failing that, to get a good foundation in one art before
branching out, or "cross training," in another.  The feeling is that the two
arts are likely to conflict with each other.  They may require differing ways
of moving your body, differing postures, differing positions, and offer
differing solutions to given situations.  These differences could serve to
confuse and frustrate the new student as he endeavors to apply what he has
learned in his classes.

After you have developed a good base in one art, you can then explore other
arts without undue confusion or overlap.

There are, however, some noted exceptions to consider.  You may want to
consider cross training in arts that have very little overlap, that complement
each other well, or that fill in gaps you may feel are missing.

Another consideration is the instructors.  Some instructors encourage cross
training or even teach multiple arts themselves while other instructors
strongly discourage cross training and may be upset to find a student cross
training.  If cross training interests you, you should talk with the
instructors of each art to see how they feel about it before you start taking
classes there.  They may already have a program in place or may be able to
make recommendations.

Further, cross training, even if it is advantageous and encouraged will
usually slow your advancement in each art far more then if you were to
dedicate all of your training time to just one.

Finally, as hinted at earlier, you should consider your personal resources.
Can you afford to pay for two different classes and all the associated
fees for each?  Not only money, but, more importantly, your time resource.
You will need to dedicate a certain amount of time to the practice of each
art, both in class and out, in order to see advancement.  Do you have the
time to dedicate to each?

Some examples of arts simultaneously trained include Tae Kwon Do with Hapkido,
Muay Thai with Brazillian Ju Jitsu, and Boxing with Judo.