The answer is yes – if:

Customers are similar

It’s simply an experiment

There are no VAT implications;

Admin & time is minimal (bookkeeping, insurance etc.)

There are no unfair outcomes for shareholders.

The answer could be no if:

Your current Company is VAT registered and sells to VAT registered businesses. (If your new business sells to consumers, you may want to avoid charging them VAT).

The businesses have different investors/participators, sharing the same name causes problems.

One business offers customers credit and gets credit from suppliers – risky if they fail.

If one is asset rich – its assets could be at risk by the activities of the other business.

You really should seek advice!