Suggest is one of those verbs that cannot be followed by object + infinitive. Instead, we use that-clauses and –ing forms.
- Father suggested consulting a financial advisor. OR Father suggested that I should consult a financial advisor. (NOT Father suggested me to consult a financial advisor.) (NOT Father suggested to consult a financial advisor.)
Although should is very common in that-clauses after suggest, it can be left out.
- My Dad suggested that I learn Spanish. OR My Dad suggested that I should learn Spanish.
When the verb in the main clause is in the present tense, we can use a present tense in the that-clause after suggest. When the verb in the main clause is in the past tense, a past tense is possible in the that-clause as well.
- His doctor suggests that he stops smoking.
- His doctor suggested that he stopped smoking.
In American English, subjunctive structures are more common after suggest. Note that a subjunctive has the same form in the present tense and the past tense. It doesn’t have the –s marking in third person singular.
- The doctor suggests that he stop smoking. (Subjunctive with no –s marking.)
- The doctor suggested that he stop smoking.
In British English, subjunctive isn’t very common. Instead, British speakers use should + infinitive.
- The doctor suggests that he should stop smoking.
- The doctor suggested that he should stop smoking.
In direct suggestions that begin with I suggest…, should is not normally used.
- I suggest that you get another job. (NOT I suggest that you should get another job.)
If we have to put an indirect object after suggest we use the preposition to or for.
- Can you suggest a good dentist to me? (NOT Can you suggest me a good dentist?)