I believe you should reset the URI rules. You should be able to parse this URI OOTB.
GET /its/data/plans/{URLPARAM0}/versions/{URLPARAM1}/assets/investment is the URI.
When the REST parser parses the request the following Argument List entries should feed into the VSI:
URLPARAM0 = planid1234
URLPARAM1 = versionid1234
accountId = 4444
The Rest DPH parses the {URLPARAM...} values and creates arguments in the transaction's argument list.
The Query String (?accountId=4444) is processed OOTB and is not part of the URI in terms of URLPARAM... definition and parsing.