It depends on the reason for the dismissal of the first charge.
Here are the two most common scenarios in which multiple crimes would be charged with the initial offense being dismissed. In one case, all the charges would be subject to dismissal, in the other, the charges would stand on their own merit.
Ex. 1: A man gets pulled over for illegal window tinting and is cited. While issuing the citation the officer sees a bag of marijuana on the passenger seat and arrests the man for drug possession. Police impound the car and search the trunk, where they find unregistered fire arms, and charge the man for that crime as well.
If the man proves that his windows weren't excessively tinted and the original stop was therefore not warranted, the subsequent charges will be dropped because there was no probable cause for the search and seizure, thus violating the 4th Amendment.
Ex. 2: A man gets pulled over for drunk driving and is arrested. During the arrest, cops see 10 kilos of cocaine in the backseat. The man is then charged with DUI and Drug Possession with Intent to Distribute.
In order to get the man to plead guilty to the drug possession, the police might offer to dismiss the DUI. The dismissal of the DUI would not affect the court's ability to find the man guilty of the drug charges.
The difference here is whether the underlying case was dismissed "based on the merits" - essentially meaning, because the charge wasn't supported by law. If the charge is dismissed based on the merits, subsequent charges stemming from that arrest are likely to be unsupported as well since they lack probable cause. But if the charges are dismissed based on prosecutorial discretion (Ex. 2), there is no effect on the subsequent charges.
Every case is different and there are some exceptions to the basic rules I have outlined above. If you are facing criminal charges in a circumstance similar to what is described above, feel free to contact me to discuss the specifics of your case. www.BakerDefenseLaw.com/contact-us/