Is it grammatically correct to use the word
experience to mean multiple experiences, and follow it by a verb without adding
s. For example:
Experience show that most people ...
It is correct to use the word experience to mean multiple experiences.
But in your sentence show would be shows.
Experience shows that most people ...
The plural of "experience" is "experiences".
"Experience" can never mean more than one experience, but it can be used to describe a person or group's collective experience.
For example, on a résumé or curriculum vitae one might say "I have experience in [a particular field]" and refer to experience gained over many years and across several different job roles. If a team or a group have gained experience of a subject you can speak collectively of "their experience".
So, if you are referring to different experiences, either isolated incidents that one person experienced, or those of more than one individual, you would be correct to say:
Experiences show that most people...
However, if you are referring to just one experience or your own collective experience you should use the word in singular form but the word "show" needs to be plural:
Experience shows that most people...